Algebra Examples

$\sqrt{x + 10 - 7} = - 5$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x + 10 - 7}}^{2} = {(- 5)}^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 10 - 7}$ as ${(x + 10 - 7)}^{\frac{1}{2}}$ .

${({(x + 10 - 7)}^{\frac{1}{2}})}^{2} = {(- 5)}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(x + 10 - 7)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(x + 10 - 7)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x + 10 - 7)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(x + 10 - 7)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(x + 10 - 7)}^{1} = {(- 5)}^{2}$

Step 2.2.1.2

Subtract $7$ from $10$ .

${(x + 3)}^{1} = {(- 5)}^{2}$

Step 2.2.1.3

Simplify.

$x + 3 = {(- 5)}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $- 5$ to the power of $2$ .

$x + 3 = 25$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Subtract $3$ from both sides of the equation.

$x = 25 - 3$

Step 3.2

Subtract $3$ from $25$ .

$x = 22$

Step 4

Exclude the solutions that do not make $\sqrt{x + 10 - 7} = - 5$ true.

$No solution$