Algebra Examples

$\sqrt{x - 1} + 4 = 0$

Step 1

Subtract $4$ from both sides of the equation.

$\sqrt{x - 1} = - 4$

Step 2

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

${\sqrt{x - 1}}^{2} = {(- 4)}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

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

${({(x - 1)}^{\frac{1}{2}})}^{2} = {(- 4)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

${(x - 1)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(x - 1)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(x - 1)}^{1} = {(- 4)}^{2}$

Step 3.2.1.2

Simplify.

$x - 1 = {(- 4)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $- 4$ to the power of $2$ .

$x - 1 = 16$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$x = 16 + 1$

Step 4.2

Add $16$ and $1$ .

$x = 17$

Step 5

Exclude the solutions that do not make $\sqrt{x - 1} + 4 = 0$ true.

$No solution$