Solve by Completing the Square -4x^2-48x-20=0

$- 4 x^{2} - 48 x - 20 = 0$

Step 1

Add $20$ to both sides of the equation.

$- 4 x^{2} - 48 x = 20$

Step 2

Divide each term in $- 4 x^{2} - 48 x = 20$ by $- 4$ and simplify.

Divide each term in $- 4 x^{2} - 48 x = 20$ by $- 4$ .

$\frac{- 4 x^{2}}{- 4} + \frac{- 48 x}{- 4} = \frac{20}{- 4}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x^{2}}{- 4} + \frac{- 48 x}{- 4} = \frac{20}{- 4}$

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

$x^{2} + \frac{- 48 x}{- 4} = \frac{20}{- 4}$

Cancel the common factor of $- 48$ and $- 4$ .

Factor $- 4$ out of $- 48 x$ .

$x^{2} + \frac{- 4 (12 x)}{- 4} = \frac{20}{- 4}$

Cancel the common factors.

Factor $- 4$ out of $- 4$ .

$x^{2} + \frac{- 4 (12 x)}{- 4 (1)} = \frac{20}{- 4}$

Cancel the common factor.

$x^{2} + \frac{- 4 (12 x)}{- 4 \cdot 1} = \frac{20}{- 4}$

Rewrite the expression.

$x^{2} + \frac{12 x}{1} = \frac{20}{- 4}$

Divide $12 x$ by $1$ .

$x^{2} + 12 x = \frac{20}{- 4}$

Simplify the right side.

Divide $20$ by $- 4$ .

$x^{2} + 12 x = - 5$

Step 3

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

${(\frac{b}{2})}^{2} = {(6)}^{2}$

Step 4

Add the term to each side of the equation.

$x^{2} + 12 x + {(6)}^{2} = - 5 + {(6)}^{2}$

Step 5

Simplify the equation.

Simplify the left side.

Raise $6$ to the power of $2$ .

$x^{2} + 12 x + 36 = - 5 + {(6)}^{2}$

Simplify the right side.

Simplify $- 5 + {(6)}^{2}$ .

Raise $6$ to the power of $2$ .

$x^{2} + 12 x + 36 = - 5 + 36$

Add $- 5$ and $36$ .

$x^{2} + 12 x + 36 = 31$

Step 6

Factor the perfect trinomial square into ${(x + 6)}^{2}$ .

${(x + 6)}^{2} = 31$

Step 7

Solve the equation for $x$ .

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

$x + 6 = \pm \sqrt{31}$

Subtract $6$ from both sides of the equation.

$x = \pm \sqrt{31} - 6$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{31} - 6$

Decimal Form:

$x = - 0.43223563 \dots, - 11.56776436 \dots$

Solve by Completing the Square -4x^2-48x-20=0

Related Questions

Support LCMGCF.com by disabling your adblocker.