Trigonometry Examples

$6 = \sqrt{(- 5^{2}) + x^{2}}$

Step 1

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

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Step 1.1

Reorder $- 5^{2}$ and $x^{2}$ .

$6 = \sqrt{x^{2} - 5^{2}}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$6 = \sqrt{(x + 5) (x - 5)}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 7.81024967, 7.81024967$

Step 3