Finite Math Examples

$\sqrt{x^{2} - 10 x + 25} + 12 \sqrt{x}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $25$ as $5^{2}$ .

$\sqrt{x^{2} - 10 x + 5^{2}} + 12 \sqrt{x}$

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.

$10 x = 2 \cdot x \cdot 5$

Step 1.3

Rewrite the polynomial.

$\sqrt{x^{2} - 2 \cdot x \cdot 5 + 5^{2}} + 12 \sqrt{x}$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 5$ .

$\sqrt{{(x - 5)}^{2}} + 12 \sqrt{x}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$x - 5 + 12 \sqrt{x}$