Pre-Algebra Examples

$x^{2} + 19 x + \frac{361}{4} = 0$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $361$ as $19^{2}$ .

$x^{2} + 19 x + \frac{19^{2}}{4} = 0$

Step 1.2

Rewrite $4$ as $2^{2}$ .

$x^{2} + 19 x + \frac{19^{2}}{2^{2}} = 0$

Step 1.3

Rewrite $\frac{19^{2}}{2^{2}}$ as ${(\frac{19}{2})}^{2}$ .

$x^{2} + 19 x + {(\frac{19}{2})}^{2} = 0$

Step 1.4

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

$19 x = 2 \cdot x \cdot \frac{19}{2}$

Step 1.5

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot \frac{19}{2} + {(\frac{19}{2})}^{2} = 0$

Step 1.6

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = \frac{19}{2}$ .

${(x + \frac{19}{2})}^{2} = 0$

Step 2

Set the $x + \frac{19}{2}$ equal to $0$ .

$x + \frac{19}{2} = 0$

Step 3

Subtract $\frac{19}{2}$ from both sides of the equation.

$x = - \frac{19}{2}$