Solve for x 5(2x+1)^2=20

$5 {(2 x + 1)}^{2} = 20$

Step 1

Divide each term in $5 {(2 x + 1)}^{2} = 20$ by $5$ and simplify.

Divide each term in $5 {(2 x + 1)}^{2} = 20$ by $5$ .

$\frac{5 {(2 x + 1)}^{2}}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 {(2 x + 1)}^{2}}{5} = \frac{20}{5}$

Divide ${(2 x + 1)}^{2}$ by $1$ .

${(2 x + 1)}^{2} = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

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

Step 2

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

$2 x + 1 = \pm \sqrt{4}$

Step 3

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

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

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

$2 x + 1 = \pm 2$

Step 4

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

First, use the positive value of the $\pm$ to find the first solution.

$2 x + 1 = 2$

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

Subtract $1$ from both sides of the equation.

$2 x = 2 - 1$

Subtract $1$ from $2$ .

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$2 x + 1 = - 2$

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

Subtract $1$ from both sides of the equation.

$2 x = - 2 - 1$

Subtract $1$ from $- 2$ .

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

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

$x = \frac{1}{2}, - \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, - \frac{3}{2}$

Decimal Form:

$x = 0.5, - 1.5$

Mixed Number Form:

$x = \frac{1}{2}, - 1 \frac{1}{2}$

Solve for x 5(2x+1)^2=20

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