Algebra Examples

$\sqrt{x^{2} + 81} = x + 10$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $x$ from both sides of the equation.

$\sqrt{x^{2} + 81} - x = 10$

Step 1.2

Subtract $10$ from both sides of the equation.

$\sqrt{x^{2} + 81} - x - 10 = 0$

Step 2

Factor $- 1$ out of $\sqrt{x^{2} + 81} - x - 10$ .

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Step 2.1

Reorder $\sqrt{x^{2} + 81}$ and $- x$ .

$- x + \sqrt{x^{2} + 81} - 10 = 0$

Step 2.2

Factor $- 1$ out of $- x$ .

$- (x) + \sqrt{x^{2} + 81} - 10 = 0$

Step 2.3

Factor $- 1$ out of $\sqrt{x^{2} + 81}$ .

$- (x) - 1 (- \sqrt{x^{2} + 81}) - 10 = 0$

Step 2.4

Rewrite $- 10$ as $- 1 (10)$ .

$- (x) - 1 (- \sqrt{x^{2} + 81}) - 1 \cdot 10 = 0$

Step 2.5

Factor $- 1$ out of $- (x) - 1 (- \sqrt{x^{2} + 81})$ .

$- (x - \sqrt{x^{2} + 81}) - 1 \cdot 10 = 0$

Step 2.6

Factor $- 1$ out of $- (x - \sqrt{x^{2} + 81}) - 1 (10)$ .

$- (x - \sqrt{x^{2} + 81} + 10) = 0$