Solve by Completing the Square 4x^2+16x=20

$4 x^{2} + 16 x = 20$

Step 1

Divide each term in $4 x^{2} + 16 x = 20$ by $4$ and simplify.

Divide each term in $4 x^{2} + 16 x = 20$ by $4$ .

$\frac{4 x^{2}}{4} + \frac{16 x}{4} = \frac{20}{4}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} + \frac{16 x}{4} = \frac{20}{4}$

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{16 x}{4} = \frac{20}{4}$

Cancel the common factor of $16$ and $4$ .

Factor $4$ out of $16 x$ .

$x^{2} + \frac{4 (4 x)}{4} = \frac{20}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$x^{2} + \frac{4 (4 x)}{4 (1)} = \frac{20}{4}$

Cancel the common factor.

$x^{2} + \frac{4 (4 x)}{4 \cdot 1} = \frac{20}{4}$

Rewrite the expression.

$x^{2} + \frac{4 x}{1} = \frac{20}{4}$

Divide $4 x$ by $1$ .

$x^{2} + 4 x = \frac{20}{4}$

Simplify the right side.

Divide $20$ by $4$ .

$x^{2} + 4 x = 5$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(2)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 4 x + {(2)}^{2} = 5 + {(2)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$x^{2} + 4 x + 4 = 5 + {(2)}^{2}$

Simplify the right side.

Simplify $5 + {(2)}^{2}$ .

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

$x^{2} + 4 x + 4 = 5 + 4$

Add $5$ and $4$ .

$x^{2} + 4 x + 4 = 9$

Step 5

Factor the perfect trinomial square into ${(x + 2)}^{2}$ .

${(x + 2)}^{2} = 9$

Step 6

Solve the equation for $x$ .

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

$x + 2 = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x + 2 = \pm \sqrt{3^{2}}$

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

$x + 2 = \pm 3$

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.

$x + 2 = 3$

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

Subtract $2$ from both sides of the equation.

$x = 3 - 2$

Subtract $2$ from $3$ .

$x = 1$

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

$x + 2 = - 3$

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

Subtract $2$ from both sides of the equation.

$x = - 3 - 2$

Subtract $2$ from $- 3$ .

$x = - 5$

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

$x = 1, - 5$

Solve by Completing the Square 4x^2+16x=20

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