Math

Question Solve the equation 5=(x+7)1211-5=(x+7)^{\frac{1}{2}}-11 for the value of xx.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 5=(x+7)1211-5=(x+7)^{\frac{1}{2}}-11.
2. We need to solve for xx.
3. The term (x+7)12(x+7)^{\frac{1}{2}} represents the square root of x+7x+7.

STEP 2

First, we will isolate the square root term on one side of the equation by adding 11 to both sides.
5+11=(x+7)1211+11-5 + 11 = (x+7)^{\frac{1}{2}} - 11 + 11

STEP 3

Perform the addition on both sides of the equation.
6=(x+7)126 = (x+7)^{\frac{1}{2}}

STEP 4

To remove the square root, we will square both sides of the equation.
(6)2=((x+7)12)2(6)^2 = ((x+7)^{\frac{1}{2}})^2

STEP 5

Calculate the square of 6 and apply the property that squaring the square root of a number gives us the original number.
36=x+736 = x + 7

STEP 6

Now, we will isolate xx by subtracting 7 from both sides of the equation.
367=x+7736 - 7 = x + 7 - 7

STEP 7

Perform the subtraction on both sides of the equation.
29=x29 = x
The solution to the equation 5=(x+7)1211-5=(x+7)^{\frac{1}{2}}-11 is x=29x = 29.

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