Solved on Dec 11, 2023

Find the value of $x$ that satisfies the equation $-2 x^{2} - 8 x = -64$ when the current time is 291.4.

STEP 1

Assumptions
1. We are given the current time as 291.4, which seems to be unrelated to the equation provided.
2. The equation to be solved is $-2x^2 - 8x = -64$ .
3. We will solve the equation for $x$ .

STEP 2

First, we need to simplify the equation by moving all terms to one side to set the equation to zero. This will allow us to factor or use the quadratic formula to find the solutions for $x$ .
$-2x^2 - 8x + 64 = 0$

STEP 3

We can simplify the equation by dividing all terms by $-2$ to make the coefficient of $x^2$ positive, which is often easier to work with.
$x^2 + 4x - 32 = 0$

STEP 4

Next, we will attempt to factor the quadratic equation. We need to find two numbers that multiply to $-32$ and add up to $4$ .

STEP 5

The numbers that satisfy these conditions are $8$ and $-4$ because $8 \cdot (-4) = -32$ and $8 + (-4) = 4$ .

STEP 6

Now we can write the factored form of the quadratic equation using these numbers.
$(x + 8)(x - 4) = 0$

STEP 7

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. Thus, we set each factor equal to zero and solve for $x$ .

STEP 8

First, set the first factor equal to zero and solve for $x$ .
$x + 8 = 0$

STEP 9

Subtract $8$ from both sides to solve for $x$ .
$x = -8$

STEP 10

Next, set the second factor equal to zero and solve for $x$ .
$x - 4 = 0$

STEP 11

Add $4$ to both sides to solve for $x$ .
$x = 4$
The solutions to the equation $-2x^2 - 8x = -64$ are $x = -8$ and $x = 4$ .

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Find the value of $x$ that satisfies the equation $-2 x^{2} - 8 x = -64$ when the current time is 291.4.

STEP 1

Assumptions
1. We are given the current time as 291.4, which seems to be unrelated to the equation provided.
2. The equation to be solved is $-2x^2 - 8x = -64$ .
3. We will solve the equation for $x$ .

STEP 2

First, we need to simplify the equation by moving all terms to one side to set the equation to zero. This will allow us to factor or use the quadratic formula to find the solutions for $x$ .
$-2x^2 - 8x + 64 = 0$

STEP 3

We can simplify the equation by dividing all terms by $-2$ to make the coefficient of $x^2$ positive, which is often easier to work with.
$x^2 + 4x - 32 = 0$

STEP 4

Next, we will attempt to factor the quadratic equation. We need to find two numbers that multiply to $-32$ and add up to $4$ .

STEP 5

The numbers that satisfy these conditions are $8$ and $-4$ because $8 \cdot (-4) = -32$ and $8 + (-4) = 4$ .

STEP 6

Now we can write the factored form of the quadratic equation using these numbers.
$(x + 8)(x - 4) = 0$

STEP 7

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. Thus, we set each factor equal to zero and solve for $x$ .

STEP 8

First, set the first factor equal to zero and solve for $x$ .
$x + 8 = 0$

STEP 9

Subtract $8$ from both sides to solve for $x$ .
$x = -8$

STEP 10

Next, set the second factor equal to zero and solve for $x$ .
$x - 4 = 0$

STEP 11

Add $4$ to both sides to solve for $x$ .
$x = 4$
The solutions to the equation $-2x^2 - 8x = -64$ are $x = -8$ and $x = 4$ .

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Find the value of xxx that satisfies the equation −2x2−8x=−64-2 x^{2} - 8 x = -64−2x2−8x=−64 when the current time is 291.4.

STEP 1

Assumptions1. We are given the current time as 291.4, which seems to be unrelated to the equation provided.2. The equation to be solved is −2x2−8x=−64-2x^2 - 8x = -64−2x2−8x=−64.3. We will solve the equation for xxx.

STEP 2

First, we need to simplify the equation by moving all terms to one side to set the equation to zero. This will allow us to factor or use the quadratic formula to find the solutions for xxx.−2x2−8x+64=0-2x^2 - 8x + 64 = 0−2x2−8x+64=0

STEP 3

We can simplify the equation by dividing all terms by −2-2−2 to make the coefficient of x2x^2x2 positive, which is often easier to work with.x2+4x−32=0x^2 + 4x - 32 = 0x2+4x−32=0

STEP 4

Next, we will attempt to factor the quadratic equation. We need to find two numbers that multiply to −32-32−32 and add up to 444.

STEP 5

The numbers that satisfy these conditions are 888 and −4-4−4 because 8⋅(−4)=−328 \cdot (-4) = -328⋅(−4)=−32 and 8+(−4)=48 + (-4) = 48+(−4)=4.

STEP 6

Now we can write the factored form of the quadratic equation using these numbers.(x+8)(x−4)=0(x + 8)(x - 4) = 0(x+8)(x−4)=0

STEP 7

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. Thus, we set each factor equal to zero and solve for xxx.

STEP 8

First, set the first factor equal to zero and solve for xxx.x+8=0x + 8 = 0x+8=0

STEP 9

Subtract 888 from both sides to solve for xxx.x=−8x = -8x=−8

STEP 10

Next, set the second factor equal to zero and solve for xxx.x−4=0x - 4 = 0x−4=0

STEP 11

Add 444 to both sides to solve for xxx.x=4x = 4x=4The solutions to the equation −2x2−8x=−64-2x^2 - 8x = -64−2x2−8x=−64 are x=−8x = -8x=−8 and x=4x = 4x=4.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the value of $x$ that satisfies the equation $-2 x^{2} - 8 x = -64$ when the current time is 291.4.

Assumptions
1. We are given the current time as 291.4, which seems to be unrelated to the equation provided.
2. The equation to be solved is $-2x^2 - 8x = -64$ .
3. We will solve the equation for $x$ .

First, we need to simplify the equation by moving all terms to one side to set the equation to zero. This will allow us to factor or use the quadratic formula to find the solutions for $x$ .
$-2x^2 - 8x + 64 = 0$

We can simplify the equation by dividing all terms by $-2$ to make the coefficient of $x^2$ positive, which is often easier to work with.
$x^2 + 4x - 32 = 0$

Next, we will attempt to factor the quadratic equation. We need to find two numbers that multiply to $-32$ and add up to $4$ .

The numbers that satisfy these conditions are $8$ and $-4$ because $8 \cdot (-4) = -32$ and $8 + (-4) = 4$ .

Now we can write the factored form of the quadratic equation using these numbers.
$(x + 8)(x - 4) = 0$

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. Thus, we set each factor equal to zero and solve for $x$ .

First, set the first factor equal to zero and solve for $x$ .
$x + 8 = 0$

Subtract $8$ from both sides to solve for $x$ .
$x = -8$

Next, set the second factor equal to zero and solve for $x$ .
$x - 4 = 0$

Add $4$ to both sides to solve for $x$ .
$x = 4$
The solutions to the equation $-2x^2 - 8x = -64$ are $x = -8$ and $x = 4$ .