Solved on Feb 16, 2024

Solve for $x$ in $G(x)=x^{2}+5x-22$ . If $G(x)=-8$ , then $x=$

STEP 1

Assumptions
1. The function is given as $G(x)=x^{2}+5x-22$ .
2. We are given that $G(x)=-8$ .
3. We need to solve for $x$ .

STEP 2

Set the function $G(x)$ equal to $-8$ to find the values of $x$ that satisfy the equation.
$G(x) = x^{2} + 5x - 22 = -8$

STEP 3

To solve for $x$ , we need to move all terms to one side of the equation to set it equal to zero. Add $8$ to both sides of the equation.
$x^{2} + 5x - 22 + 8 = 0$

STEP 4

Combine like terms on the left side of the equation.
$x^{2} + 5x - 14 = 0$

STEP 5

Now we have a quadratic equation in standard form. We will attempt to factor the quadratic equation.

STEP 6

Look for two numbers that multiply to $-14$ and add to $5$ . The numbers $7$ and $-2$ satisfy these conditions.

STEP 7

Factor the quadratic equation using these two numbers.
$(x + 7)(x - 2) = 0$

STEP 8

Apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero.
$x + 7 = 0 \quad \text{or} \quad x - 2 = 0$

STEP 9

Solve each equation for $x$ .
For the first equation:
$x + 7 = 0$
$x = -7$
For the second equation:
$x - 2 = 0$
$x = 2$

STEP 10

The solutions to the equation are $x = -7$ and $x = 2$ .
$x = -7, 2$

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Solve for $x$ in $G(x)=x^{2}+5x-22$ . If $G(x)=-8$ , then $x=$

STEP 1

Assumptions
1. The function is given as $G(x)=x^{2}+5x-22$ .
2. We are given that $G(x)=-8$ .
3. We need to solve for $x$ .

STEP 2

Set the function $G(x)$ equal to $-8$ to find the values of $x$ that satisfy the equation.
$G(x) = x^{2} + 5x - 22 = -8$

STEP 3

To solve for $x$ , we need to move all terms to one side of the equation to set it equal to zero. Add $8$ to both sides of the equation.
$x^{2} + 5x - 22 + 8 = 0$

STEP 4

Combine like terms on the left side of the equation.
$x^{2} + 5x - 14 = 0$

STEP 5

Now we have a quadratic equation in standard form. We will attempt to factor the quadratic equation.

STEP 6

Look for two numbers that multiply to $-14$ and add to $5$ . The numbers $7$ and $-2$ satisfy these conditions.

STEP 7

Factor the quadratic equation using these two numbers.
$(x + 7)(x - 2) = 0$

STEP 8

Apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero.
$x + 7 = 0 \quad \text{or} \quad x - 2 = 0$

STEP 9

Solve each equation for $x$ .
For the first equation:
$x + 7 = 0$
$x = -7$
For the second equation:
$x - 2 = 0$
$x = 2$

STEP 10

The solutions to the equation are $x = -7$ and $x = 2$ .
$x = -7, 2$

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Solve for xxx in G(x)=x2+5x−22G(x)=x^{2}+5x-22G(x)=x2+5x−22. If G(x)=−8G(x)=-8G(x)=−8, then x=x=x=

STEP 1

Assumptions1. The function is given as G(x)=x2+5x−22G(x)=x^{2}+5x-22G(x)=x2+5x−22.2. We are given that G(x)=−8G(x)=-8G(x)=−8.3. We need to solve for xxx.

STEP 2

Set the function G(x)G(x)G(x) equal to −8-8−8 to find the values of xxx that satisfy the equation.G(x)=x2+5x−22=−8G(x) = x^{2} + 5x - 22 = -8G(x)=x2+5x−22=−8

STEP 3

To solve for xxx, we need to move all terms to one side of the equation to set it equal to zero. Add 888 to both sides of the equation.x2+5x−22+8=0x^{2} + 5x - 22 + 8 = 0x2+5x−22+8=0

STEP 4

Combine like terms on the left side of the equation.x2+5x−14=0x^{2} + 5x - 14 = 0x2+5x−14=0

STEP 5

Now we have a quadratic equation in standard form. We will attempt to factor the quadratic equation.

STEP 6

Look for two numbers that multiply to −14-14−14 and add to 555. The numbers 777 and −2-2−2 satisfy these conditions.

STEP 7

Factor the quadratic equation using these two numbers.(x+7)(x−2)=0(x + 7)(x - 2) = 0(x+7)(x−2)=0

STEP 8

Apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero.x+7=0orx−2=0x + 7 = 0 \quad \text{or} \quad x - 2 = 0x+7=0orx−2=0

STEP 9

Solve each equation for xxx.For the first equation:x+7=0x + 7 = 0x+7=0x=−7x = -7x=−7For the second equation:x−2=0x - 2 = 0x−2=0x=2x = 2x=2

STEP 10

The solutions to the equation are x=−7x = -7x=−7 and x=2x = 2x=2.x=−7,2x = -7, 2x=−7,2

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Solve for $x$ in $G(x)=x^{2}+5x-22$ . If $G(x)=-8$ , then $x=$

Assumptions
1. The function is given as $G(x)=x^{2}+5x-22$ .
2. We are given that $G(x)=-8$ .
3. We need to solve for $x$ .

Set the function $G(x)$ equal to $-8$ to find the values of $x$ that satisfy the equation.
$G(x) = x^{2} + 5x - 22 = -8$

To solve for $x$ , we need to move all terms to one side of the equation to set it equal to zero. Add $8$ to both sides of the equation.
$x^{2} + 5x - 22 + 8 = 0$

Combine like terms on the left side of the equation.
$x^{2} + 5x - 14 = 0$

Look for two numbers that multiply to $-14$ and add to $5$ . The numbers $7$ and $-2$ satisfy these conditions.

Factor the quadratic equation using these two numbers.
$(x + 7)(x - 2) = 0$

Apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero.
$x + 7 = 0 \quad \text{or} \quad x - 2 = 0$

Solve each equation for $x$ .
For the first equation:
$x + 7 = 0$
$x = -7$
For the second equation:
$x - 2 = 0$
$x = 2$

The solutions to the equation are $x = -7$ and $x = 2$ .
$x = -7, 2$