Solve by Completing the Square 0=3x^2-12x-15

$0 = 3 x^{2} - 12 x - 15$

Step 1

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

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 x^{2} - 12 x - 15 = 0$

Add $15$ to both sides of the equation.

$3 x^{2} - 12 x = 15$

Step 2

Divide each term in $3 x^{2} - 12 x = 15$ by $3$ and simplify.

Divide each term in $3 x^{2} - 12 x = 15$ by $3$ .

$\frac{3 x^{2}}{3} + \frac{- 12 x}{3} = \frac{15}{3}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} + \frac{- 12 x}{3} = \frac{15}{3}$

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

$x^{2} + \frac{- 12 x}{3} = \frac{15}{3}$

Cancel the common factor of $- 12$ and $3$ .

Factor $3$ out of $- 12 x$ .

$x^{2} + \frac{3 (- 4 x)}{3} = \frac{15}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$x^{2} + \frac{3 (- 4 x)}{3 (1)} = \frac{15}{3}$

Cancel the common factor.

$x^{2} + \frac{3 (- 4 x)}{3 \cdot 1} = \frac{15}{3}$

Rewrite the expression.

$x^{2} + \frac{- 4 x}{1} = \frac{15}{3}$

Divide $- 4 x$ by $1$ .

$x^{2} - 4 x = \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

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

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 $b$ .

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

Step 4

Add the term to each side of the equation.

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

Step 5

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 6

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

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

Step 7

Solve the equation for $x$ .

Take the square 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.

Add $2$ to both sides of the equation.

$x = 3 + 2$

Add $3$ and $2$ .

$x = 5$

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.

Add $2$ to both sides of the equation.

$x = - 3 + 2$

Add $- 3$ and $2$ .

$x = - 1$

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

$x = 5, - 1$

Solve by Completing the Square 0=3x^2-12x-15

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