Algebra Examples

$6 x^{2} + 96 x = - 384$

Step 1

Add $384$ to both sides of the equation.

$6 x^{2} + 96 x + 384 = 0$

Step 2

Factor $6$ out of $6 x^{2} + 96 x + 384$ .

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Step 2.1

Factor $6$ out of $6 x^{2}$ .

$6 (x^{2}) + 96 x + 384 = 0$

Step 2.2

Factor $6$ out of $96 x$ .

$6 (x^{2}) + 6 (16 x) + 384 = 0$

Step 2.3

Factor $6$ out of $384$ .

$6 x^{2} + 6 (16 x) + 6 \cdot 64 = 0$

Step 2.4

Factor $6$ out of $6 x^{2} + 6 (16 x)$ .

$6 (x^{2} + 16 x) + 6 \cdot 64 = 0$

Step 2.5

Factor $6$ out of $6 (x^{2} + 16 x) + 6 \cdot 64$ .

$6 (x^{2} + 16 x + 64) = 0$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $64$ as $8^{2}$ .

$6 (x^{2} + 16 x + 8^{2}) = 0$

Step 3.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$16 x = 2 \cdot x \cdot 8$

Step 3.3

Rewrite the polynomial.

$6 (x^{2} + 2 \cdot x \cdot 8 + 8^{2}) = 0$

Step 3.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 8$ .

$6 {(x + 8)}^{2} = 0$

Step 4

Divide each term in $6 {(x + 8)}^{2} = 0$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 {(x + 8)}^{2} = 0$ by $6$ .

$\frac{6 {(x + 8)}^{2}}{6} = \frac{0}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 {(x + 8)}^{2}}{6} = \frac{0}{6}$

Step 4.2.1.2

Divide ${(x + 8)}^{2}$ by $1$ .

${(x + 8)}^{2} = \frac{0}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $6$ .

${(x + 8)}^{2} = 0$

Step 5

Set the $x + 8$ equal to $0$ .

$x + 8 = 0$

Step 6

Subtract $8$ from both sides of the equation.

$x = - 8$