Algebra Examples

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

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

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

x - 1 = \pm \sqrt{4}

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

Step 2

Simplify

\pm \sqrt{4}

$\pm \sqrt{4}$ .

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Step 2.1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

x - 1 = \pm \sqrt{2^{2}}

$x - 1 = \pm \sqrt{2^{2}}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$x - 1 = \pm 2$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the

$\pm$ to find the first solution.

$x - 1 = 2$

Step 3.2

Move all terms not containing

$x$ to the right side of the equation.

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Step 3.2.1

Add

$1$ to both sides of the equation.

$x = 2 + 1$

Step 3.2.2

Add

$2$ and

$1$ .

$x = 3$

Step 3.3

Next, use the negative value of the

$\pm$ to find the second solution.

$x - 1 = - 2$

Step 3.4

Move all terms not containing

$x$ to the right side of the equation.

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Step 3.4.1

Add

$1$ to both sides of the equation.

$x = - 2 + 1$

Step 3.4.2

Add

$- 2$ and

$1$ .

$x = - 1$

Step 3.5

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 1$

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

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