Math

Question Solve for xx in the equation x8+2=7\sqrt{x-8}+2=7. The solutions are x=1,13,17,33x=1, 13, 17, 33.

Studdy Solution

STEP 1

Assumptions1. The equation is x8+=7\sqrt{x-8}+=7 . We are solving for xx
3. The square root function is defined for x8x \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.
x8+22=72\sqrt{x-8}+2-2=7-2

STEP 3

implify the equation.
x8=5\sqrt{x-8}=5

STEP 4

To get rid of the square root, we can square both sides of the equation.
(x8)2=2(\sqrt{x-8})^2=^2

STEP 5

implify the equation.
x8=25x-8=25

STEP 6

Now, we can solve for xx by adding8 to both sides of the equation.
x8+8=25+8x-8+8=25+8

STEP 7

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

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