Solve by Completing the Square 4x^2+24x=4

$4 x^{2} + 24 x = 4$

Step 1

Divide each term in $4 x^{2} + 24 x = 4$ by $4$ and simplify.

Divide each term in $4 x^{2} + 24 x = 4$ by $4$ .

$\frac{4 x^{2}}{4} + \frac{24 x}{4} = \frac{4}{4}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} + \frac{24 x}{4} = \frac{4}{4}$

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

$x^{2} + \frac{24 x}{4} = \frac{4}{4}$

Cancel the common factor of $24$ and $4$ .

Factor $4$ out of $24 x$ .

$x^{2} + \frac{4 (6 x)}{4} = \frac{4}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$x^{2} + \frac{4 (6 x)}{4 (1)} = \frac{4}{4}$

Cancel the common factor.

$x^{2} + \frac{4 (6 x)}{4 \cdot 1} = \frac{4}{4}$

Rewrite the expression.

$x^{2} + \frac{6 x}{1} = \frac{4}{4}$

Divide $6 x$ by $1$ .

$x^{2} + 6 x = \frac{4}{4}$

Simplify the right side.

Divide $4$ by $4$ .

$x^{2} + 6 x = 1$

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 $b$ .

${(\frac{b}{2})}^{2} = {(3)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 6 x + {(3)}^{2} = 1 + {(3)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = 1 + {(3)}^{2}$

Simplify the right side.

Simplify $1 + {(3)}^{2}$ .

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = 1 + 9$

Add $1$ and $9$ .

$x^{2} + 6 x + 9 = 10$

Step 5

Factor the perfect trinomial square into ${(x + 3)}^{2}$ .

${(x + 3)}^{2} = 10$

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.

$x + 3 = \pm \sqrt{10}$

Subtract $3$ from both sides of the equation.

$x = \pm \sqrt{10} - 3$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{10} - 3$

Decimal Form:

$x = 0.16227766 \dots, - 6.16227766 \dots$

Solve by Completing the Square 4x^2+24x=4

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