Solved on Dec 08, 2023

Solve the quadratic equation $10=x^{2}-3x$ for the value of $x$ .

STEP 1

Assumptions
1. We have the equation $10 = x^{2} - 3x$ .
2. We need to solve for the variable $x$ .

STEP 2

To solve the quadratic equation, we first need to set it to zero. We can do this by subtracting 10 from both sides of the equation.
$x^{2} - 3x - 10 = 0$

STEP 3

Next, we try to factor the quadratic if possible. We look for two numbers that multiply to give -10 and add to give -3.

STEP 4

We find that the numbers -5 and 2 satisfy the conditions because $(-5) \cdot 2 = -10$ and $(-5) + 2 = -3$ .

STEP 5

We can now write the quadratic equation as a product of two binomials using these numbers.
$(x - 5)(x + 2) = 0$

STEP 6

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero.

STEP 7

We set each factor equal to zero and solve for $x$ .
$x - 5 = 0 \quad \text{or} \quad x + 2 = 0$

STEP 8

Solve the first equation for $x$ .
$x = 5$

STEP 9

Solve the second equation for $x$ .
$x = -2$

STEP 10

We have found the two solutions to the quadratic equation.
The solutions are $x = 5$ and $x = -2$ .

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Solve the quadratic equation $10=x^{2}-3x$ for the value of $x$ .

STEP 1

Assumptions
1. We have the equation $10 = x^{2} - 3x$ .
2. We need to solve for the variable $x$ .

STEP 2

To solve the quadratic equation, we first need to set it to zero. We can do this by subtracting 10 from both sides of the equation.
$x^{2} - 3x - 10 = 0$

STEP 3

Next, we try to factor the quadratic if possible. We look for two numbers that multiply to give -10 and add to give -3.

STEP 4

We find that the numbers -5 and 2 satisfy the conditions because $(-5) \cdot 2 = -10$ and $(-5) + 2 = -3$ .

STEP 5

We can now write the quadratic equation as a product of two binomials using these numbers.
$(x - 5)(x + 2) = 0$

STEP 6

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero.

STEP 7

We set each factor equal to zero and solve for $x$ .
$x - 5 = 0 \quad \text{or} \quad x + 2 = 0$

STEP 8

Solve the first equation for $x$ .
$x = 5$

STEP 9

Solve the second equation for $x$ .
$x = -2$

STEP 10

We have found the two solutions to the quadratic equation.
The solutions are $x = 5$ and $x = -2$ .

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Solve the quadratic equation 10=x2−3x10=x^{2}-3x10=x2−3x for the value of xxx.

STEP 1

Assumptions1. We have the equation 10=x2−3x10 = x^{2} - 3x10=x2−3x.2. We need to solve for the variable xxx.

STEP 2

To solve the quadratic equation, we first need to set it to zero. We can do this by subtracting 10 from both sides of the equation.x2−3x−10=0x^{2} - 3x - 10 = 0x2−3x−10=0

STEP 3

Next, we try to factor the quadratic if possible. We look for two numbers that multiply to give -10 and add to give -3.

STEP 4

We find that the numbers -5 and 2 satisfy the conditions because (−5)⋅2=−10(-5) \cdot 2 = -10(−5)⋅2=−10 and (−5)+2=−3(-5) + 2 = -3(−5)+2=−3.

STEP 5

We can now write the quadratic equation as a product of two binomials using these numbers.(x−5)(x+2)=0(x - 5)(x + 2) = 0(x−5)(x+2)=0

STEP 6

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero.

STEP 7

We set each factor equal to zero and solve for xxx.x−5=0orx+2=0x - 5 = 0 \quad \text{or} \quad x + 2 = 0x−5=0orx+2=0

STEP 8

Solve the first equation for xxx.x=5x = 5x=5

STEP 9

Solve the second equation for xxx.x=−2x = -2x=−2

STEP 10

We have found the two solutions to the quadratic equation.The solutions are x=5x = 5x=5 and x=−2x = -2x=−2.

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

Solve the quadratic equation $10=x^{2}-3x$ for the value of $x$ .

Assumptions
1. We have the equation $10 = x^{2} - 3x$ .
2. We need to solve for the variable $x$ .

To solve the quadratic equation, we first need to set it to zero. We can do this by subtracting 10 from both sides of the equation.
$x^{2} - 3x - 10 = 0$

We find that the numbers -5 and 2 satisfy the conditions because $(-5) \cdot 2 = -10$ and $(-5) + 2 = -3$ .

We can now write the quadratic equation as a product of two binomials using these numbers.
$(x - 5)(x + 2) = 0$

We set each factor equal to zero and solve for $x$ .
$x - 5 = 0 \quad \text{or} \quad x + 2 = 0$

Solve the first equation for $x$ .
$x = 5$

Solve the second equation for $x$ .
$x = -2$

We have found the two solutions to the quadratic equation.
The solutions are $x = 5$ and $x = -2$ .