Solved on Nov 07, 2023

Solve for $x$ in the equation $\sqrt{x-8}+2=7$ . The solutions are $x=1, 13, 17, 33$ .

STEP 1

Assumptions1. The equation is $\sqrt{x-8}+=7$ . We are solving for $x$
3. The square root function is defined for $x \geq8$ because we cannot take the square root of a negative number

STEP 2

First, we want to isolate the square root term. We can do this by subtracting2 from both sides of the equation.
$\sqrt{x-8}+2-2=7-2$

STEP 3

implify the equation.
$\sqrt{x-8}=5$

STEP 4

To get rid of the square root, we can square both sides of the equation.
$(\sqrt{x-8})^2=^2$

STEP 5

implify the equation.
$x-8=25$

STEP 6

Now, we can solve for $x$ by adding8 to both sides of the equation.
$x-8+8=25+8$

STEP 7

implify the equation to find the value of $x$ .
$x=33$ So, the solution to the equation $\sqrt{x-}+2=7$ is $x=33$ .

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Solve for $x$ in the equation $\sqrt{x-8}+2=7$ . The solutions are $x=1, 13, 17, 33$ .

STEP 1

Assumptions1. The equation is $\sqrt{x-8}+=7$ . We are solving for $x$
3. The square root function is defined for $x \geq8$ because we cannot take the square root of a negative number

STEP 2

First, we want to isolate the square root term. We can do this by subtracting2 from both sides of the equation.
$\sqrt{x-8}+2-2=7-2$

STEP 3

implify the equation.
$\sqrt{x-8}=5$

STEP 4

To get rid of the square root, we can square both sides of the equation.
$(\sqrt{x-8})^2=^2$

STEP 5

implify the equation.
$x-8=25$

STEP 6

Now, we can solve for $x$ by adding8 to both sides of the equation.
$x-8+8=25+8$

STEP 7

implify the equation to find the value of $x$ .
$x=33$ So, the solution to the equation $\sqrt{x-}+2=7$ is $x=33$ .

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Solve for xxx in the equation x−8+2=7\sqrt{x-8}+2=7x−8​+2=7. The solutions are x=1,13,17,33x=1, 13, 17, 33x=1,13,17,33.

STEP 1

Assumptions1. The equation is x−8+=7\sqrt{x-8}+=7x−8​+=7 . We are solving for xxx3. The square root function is defined for x≥8x \geq8x≥8 because we cannot take the square root of a negative number

STEP 2

First, we want to isolate the square root term. We can do this by subtracting2 from both sides of the equation.x−8+2−2=7−2\sqrt{x-8}+2-2=7-2x−8​+2−2=7−2

STEP 3

implify the equation.x−8=5\sqrt{x-8}=5x−8​=5

STEP 4

To get rid of the square root, we can square both sides of the equation.(x−8)2=2(\sqrt{x-8})^2=^2(x−8​)2=2

STEP 5

implify the equation.x−8=25x-8=25x−8=25

STEP 6

Now, we can solve for xxx by adding8 to both sides of the equation.x−8+8=25+8x-8+8=25+8x−8+8=25+8

STEP 7

implify the equation to find the value of xxx.x=33x=33x=33So, the solution to the equation x−+2=7\sqrt{x-}+2=7x−​+2=7 is x=33x=33x=33.

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Solve for $x$ in the equation $\sqrt{x-8}+2=7$ . The solutions are $x=1, 13, 17, 33$ .

Assumptions1. The equation is $\sqrt{x-8}+=7$ . We are solving for $x$
3. The square root function is defined for $x \geq8$ because we cannot take the square root of a negative number

First, we want to isolate the square root term. We can do this by subtracting2 from both sides of the equation.
$\sqrt{x-8}+2-2=7-2$

implify the equation.
$\sqrt{x-8}=5$

To get rid of the square root, we can square both sides of the equation.
$(\sqrt{x-8})^2=^2$

implify the equation.
$x-8=25$

Now, we can solve for $x$ by adding8 to both sides of the equation.
$x-8+8=25+8$

implify the equation to find the value of $x$ .
$x=33$ So, the solution to the equation $\sqrt{x-}+2=7$ is $x=33$ .