Solve by Completing the Square 4x^2-72=24x

$4 x^{2} - 72 = 24 x$

Step 1

Simplify the equation into a proper form to complete the square.

Add $72$ to both sides of the equation.

$4 x^{2} = 24 x + 72$

Subtract $24 x$ from both sides of the equation.

$4 x^{2} - 24 x = 72$

Step 2

Divide each term in $4 x^{2} - 24 x = 72$ by $4$ and simplify.

Divide each term in $4 x^{2} - 24 x = 72$ by $4$ .

$\frac{4 x^{2}}{4} + \frac{- 24 x}{4} = \frac{72}{4}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} + \frac{- 24 x}{4} = \frac{72}{4}$

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

$x^{2} + \frac{- 24 x}{4} = \frac{72}{4}$

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

Factor $4$ out of $- 24 x$ .

$x^{2} + \frac{4 (- 6 x)}{4} = \frac{72}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$x^{2} + \frac{4 (- 6 x)}{4 (1)} = \frac{72}{4}$

Cancel the common factor.

$x^{2} + \frac{4 (- 6 x)}{4 \cdot 1} = \frac{72}{4}$

Rewrite the expression.

$x^{2} + \frac{- 6 x}{1} = \frac{72}{4}$

Divide $- 6 x$ by $1$ .

$x^{2} - 6 x = \frac{72}{4}$

Simplify the right side.

Divide $72$ by $4$ .

$x^{2} - 6 x = 18$

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 $b$ .

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

Step 4

Add the term to each side of the equation.

$x^{2} - 6 x + {(- 3)}^{2} = 18 + {(- 3)}^{2}$

Step 5

Simplify the equation.

Simplify the left side.

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

$x^{2} - 6 x + 9 = 18 + {(- 3)}^{2}$

Simplify the right side.

Simplify $18 + {(- 3)}^{2}$ .

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

$x^{2} - 6 x + 9 = 18 + 9$

Add $18$ and $9$ .

$x^{2} - 6 x + 9 = 27$

Step 6

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

${(x - 3)}^{2} = 27$

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.

$x - 3 = \pm \sqrt{27}$

Simplify $\pm \sqrt{27}$ .

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$x - 3 = \pm \sqrt{9 (3)}$

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

$x - 3 = \pm \sqrt{3^{2} \cdot 3}$

Pull terms out from under the radical.

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

Add $3$ to both sides of the equation.

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 8.19615242 \dots, - 2.19615242 \dots$

Solve by Completing the Square 4x^2-72=24x

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