Question Solve the quadratic equation $-8(x-2)(x-7)=0$ to find the values of $x$ .

Studdy Solution

STEP 1

Assumptions
1. The equation is given as $-8(x-2)(x-7)=0$ .
2. We need to find the values of $x$ that satisfy the equation.

STEP 2

The equation is a product of terms equal to zero. According to the zero product property, if the product of multiple terms is zero, then at least one of the terms must be zero.

STEP 3

Set each term in the product equal to zero separately.
$-8 = 0, \quad (x-2) = 0, \quad (x-7) = 0$

STEP 4

Solve the first equation $-8 = 0$ .
This equation is not true for any value of $x$ because $-8$ is a constant and cannot equal zero. Therefore, we can ignore this term.

STEP 5

Solve the second equation $(x-2) = 0$ .
$x - 2 = 0$

STEP 6

Add 2 to both sides of the equation to solve for $x$ .
$x = 2$

STEP 7

Solve the third equation $(x-7) = 0$ .
$x - 7 = 0$

STEP 8

Add 7 to both sides of the equation to solve for $x$ .
$x = 7$
The solutions to the equation $-8(x-2)(x-7)=0$ are $x = 2$ and $x = 7$ .

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Question Solve the quadratic equation $-8(x-2)(x-7)=0$ to find the values of $x$ .

Studdy Solution

STEP 1

Assumptions
1. The equation is given as $-8(x-2)(x-7)=0$ .
2. We need to find the values of $x$ that satisfy the equation.

STEP 2

The equation is a product of terms equal to zero. According to the zero product property, if the product of multiple terms is zero, then at least one of the terms must be zero.

STEP 3

Set each term in the product equal to zero separately.
$-8 = 0, \quad (x-2) = 0, \quad (x-7) = 0$

STEP 4

Solve the first equation $-8 = 0$ .
This equation is not true for any value of $x$ because $-8$ is a constant and cannot equal zero. Therefore, we can ignore this term.

STEP 5

Solve the second equation $(x-2) = 0$ .
$x - 2 = 0$

STEP 6

Add 2 to both sides of the equation to solve for $x$ .
$x = 2$

STEP 7

Solve the third equation $(x-7) = 0$ .
$x - 7 = 0$

STEP 8

Add 7 to both sides of the equation to solve for $x$ .
$x = 7$
The solutions to the equation $-8(x-2)(x-7)=0$ are $x = 2$ and $x = 7$ .

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Question Solve the quadratic equation −8(x−2)(x−7)=0-8(x-2)(x-7)=0−8(x−2)(x−7)=0 to find the values of xxx.

Studdy Solution

STEP 1

Assumptions1. The equation is given as −8(x−2)(x−7)=0-8(x-2)(x-7)=0−8(x−2)(x−7)=0.2. We need to find the values of xxx that satisfy the equation.

STEP 2

The equation is a product of terms equal to zero. According to the zero product property, if the product of multiple terms is zero, then at least one of the terms must be zero.

STEP 3

Set each term in the product equal to zero separately.−8=0,(x−2)=0,(x−7)=0-8 = 0, \quad (x-2) = 0, \quad (x-7) = 0−8=0,(x−2)=0,(x−7)=0

STEP 4

Solve the first equation −8=0-8 = 0−8=0.This equation is not true for any value of xxx because −8-8−8 is a constant and cannot equal zero. Therefore, we can ignore this term.

STEP 5

Solve the second equation (x−2)=0(x-2) = 0(x−2)=0.x−2=0x - 2 = 0x−2=0

STEP 6

Add 2 to both sides of the equation to solve for xxx.x=2x = 2x=2

STEP 7

Solve the third equation (x−7)=0(x-7) = 0(x−7)=0.x−7=0x - 7 = 0x−7=0

STEP 8

Add 7 to both sides of the equation to solve for xxx.x=7x = 7x=7The solutions to the equation −8(x−2)(x−7)=0-8(x-2)(x-7)=0−8(x−2)(x−7)=0 are x=2x = 2x=2 and x=7x = 7x=7.

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Question Solve the quadratic equation $-8(x-2)(x-7)=0$ to find the values of $x$ .

Assumptions
1. The equation is given as $-8(x-2)(x-7)=0$ .
2. We need to find the values of $x$ that satisfy the equation.

Set each term in the product equal to zero separately.
$-8 = 0, \quad (x-2) = 0, \quad (x-7) = 0$

Solve the first equation $-8 = 0$ .
This equation is not true for any value of $x$ because $-8$ is a constant and cannot equal zero. Therefore, we can ignore this term.

Solve the second equation $(x-2) = 0$ .
$x - 2 = 0$

Add 2 to both sides of the equation to solve for $x$ .
$x = 2$

Solve the third equation $(x-7) = 0$ .
$x - 7 = 0$

Add 7 to both sides of the equation to solve for $x$ .
$x = 7$
The solutions to the equation $-8(x-2)(x-7)=0$ are $x = 2$ and $x = 7$ .