QuestionSolve $g(x)=9$ by substituting into $9=2 x^{2}-5$ , then find $x^{2}=7$ for 2 solutions.

Studdy Solution

STEP 1

Assumptions1. The function $g(x)$ is given by $g(x)=x^{}-5$ . We are asked to solve for $x$ when $g(x) =9$

STEP 2

First, we substitute $g(x)$ with9 in the equation.
$9 =2x^{2} -5$

STEP 3

Next, we rearrange the equation to isolate $x^{2}$ .
$2x^{2} =9 +5$

STEP 4

implify the right side of the equation.
$2x^{2} =14$

STEP 5

Now, divide both sides of the equation by2 to solve for $x^{2}$ .
$x^{2} = \frac{14}{2}$

STEP 6

implify the right side of the equation.
$x^{2} =$

STEP 7

Finally, we take the square root of both sides to solve for $x$ . Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$x = \pm \sqrt{7}$ The solutions are $x = \sqrt{7}$ and $x = -\sqrt{7}$ .

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QuestionSolve $g(x)=9$ by substituting into $9=2 x^{2}-5$ , then find $x^{2}=7$ for 2 solutions.

Studdy Solution

STEP 1

Assumptions1. The function $g(x)$ is given by $g(x)=x^{}-5$ . We are asked to solve for $x$ when $g(x) =9$

STEP 2

First, we substitute $g(x)$ with9 in the equation.
$9 =2x^{2} -5$

STEP 3

Next, we rearrange the equation to isolate $x^{2}$ .
$2x^{2} =9 +5$

STEP 4

implify the right side of the equation.
$2x^{2} =14$

STEP 5

Now, divide both sides of the equation by2 to solve for $x^{2}$ .
$x^{2} = \frac{14}{2}$

STEP 6

implify the right side of the equation.
$x^{2} =$

STEP 7

Finally, we take the square root of both sides to solve for $x$ . Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$x = \pm \sqrt{7}$ The solutions are $x = \sqrt{7}$ and $x = -\sqrt{7}$ .

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QuestionSolve g(x)=9g(x)=9g(x)=9 by substituting into 9=2x2−59=2 x^{2}-59=2x2−5, then find x2=7x^{2}=7x2=7 for 2 solutions.

Studdy Solution

STEP 1

Assumptions1. The function g(x)g(x)g(x) is given by g(x)=x−5g(x)=x^{}-5g(x)=x−5 . We are asked to solve for xxx when g(x)=9g(x) =9g(x)=9

STEP 2

First, we substitute g(x)g(x)g(x) with9 in the equation.9=2x2−59 =2x^{2} -59=2x2−5

STEP 3

Next, we rearrange the equation to isolate x2x^{2}x2.2x2=9+52x^{2} =9 +52x2=9+5

STEP 4

implify the right side of the equation.2x2=142x^{2} =142x2=14

STEP 5

Now, divide both sides of the equation by2 to solve for x2x^{2}x2.x2=142x^{2} = \frac{14}{2}x2=214​

STEP 6

implify the right side of the equation.x2=x^{2} =x2=

STEP 7

Finally, we take the square root of both sides to solve for xxx. Remember, when we take the square root of a number, we get two solutions one positive and one negative.x=±7x = \pm \sqrt{7}x=±7​The solutions are x=7x = \sqrt{7}x=7​ and x=−7x = -\sqrt{7}x=−7​.

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QuestionSolve $g(x)=9$ by substituting into $9=2 x^{2}-5$ , then find $x^{2}=7$ for 2 solutions.

Assumptions1. The function $g(x)$ is given by $g(x)=x^{}-5$ . We are asked to solve for $x$ when $g(x) =9$

First, we substitute $g(x)$ with9 in the equation.
$9 =2x^{2} -5$

Next, we rearrange the equation to isolate $x^{2}$ .
$2x^{2} =9 +5$

implify the right side of the equation.
$2x^{2} =14$

Now, divide both sides of the equation by2 to solve for $x^{2}$ .
$x^{2} = \frac{14}{2}$

implify the right side of the equation.
$x^{2} =$

Finally, we take the square root of both sides to solve for $x$ . Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$x = \pm \sqrt{7}$ The solutions are $x = \sqrt{7}$ and $x = -\sqrt{7}$ .