Trigonometry Examples

$x^{2} - 15 x + 56.25 = 0$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $56.25$ as ${7.5}^{2}$ .

$x^{2} - 15 x + {7.5}^{2} = 0$

Step 1.2

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

$15 x = 2 \cdot x \cdot 7.5$

Step 1.3

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 7.5 + {7.5}^{2} = 0$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 7.5$ .

${(x - 7.5)}^{2} = 0$

Step 2

Set the $x - 7.5$ equal to $0$ .

$x - 7.5 = 0$

Step 3

Add $7.5$ to both sides of the equation.

$x = 7.5$