Pre-Algebra Examples

$x^{2} + 30 x + 150 = - 75$

Step 1

Add $75$ to both sides of the equation.

$x^{2} + 30 x + 150 + 75 = 0$

Step 2

Add $150$ and $75$ .

$x^{2} + 30 x + 225 = 0$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $225$ as $15^{2}$ .

$x^{2} + 30 x + 15^{2} = 0$

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.

$30 x = 2 \cdot x \cdot 15$

Step 3.3

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot 15 + 15^{2} = 0$

Step 3.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 15$ .

${(x + 15)}^{2} = 0$

Step 4

Set the $x + 15$ equal to $0$ .

$x + 15 = 0$

Step 5

Subtract $15$ from both sides of the equation.

$x = - 15$