Solved on Jan 31, 2024

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

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

Now, we will isolate $x$ by subtracting 7 from both sides of the equation.
$36 - 7 = x + 7 - 7$

STEP 7

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

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

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

Now, we will isolate $x$ by subtracting 7 from both sides of the equation.
$36 - 7 = x + 7 - 7$

STEP 7

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

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Solve the equation −5=(x+7)12−11-5=(x+7)^{\frac{1}{2}}-11−5=(x+7)21​−11 for the value of xxx.

STEP 1

Assumptions1. We are given the equation −5=(x+7)12−11-5=(x+7)^{\frac{1}{2}}-11−5=(x+7)21​−11.2. We need to solve for xxx.3. The term (x+7)12(x+7)^{\frac{1}{2}}(x+7)21​ represents the square root of x+7x+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)12−11+11-5 + 11 = (x+7)^{\frac{1}{2}} - 11 + 11−5+11=(x+7)21​−11+11

STEP 3

Perform the addition on both sides of the equation.6=(x+7)126 = (x+7)^{\frac{1}{2}}6=(x+7)21​

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(6)2=((x+7)21​)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 + 736=x+7

STEP 6

Now, we will isolate xxx by subtracting 7 from both sides of the equation.36−7=x+7−736 - 7 = x + 7 - 736−7=x+7−7

STEP 7

Perform the subtraction on both sides of the equation.29=x29 = x29=xThe solution to the equation −5=(x+7)12−11-5=(x+7)^{\frac{1}{2}}-11−5=(x+7)21​−11 is x=29x = 29x=29.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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

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

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

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

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

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

Now, we will isolate $x$ by subtracting 7 from both sides of the equation.
$36 - 7 = x + 7 - 7$

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