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# Equations with square roots Calculator

## Get detailed solutions to your math problems with our Equations with square roots step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Solved example of equations with square roots

$\sqrt{x}+\sqrt{x+7}=7$
2

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $\sqrt{x+7}$ from both sides of the equation

$\sqrt{x}=7-\sqrt{x+7}$
3

Removing the variable's exponent raising both sides of the equation to the power $2$

$x=\left(7-\sqrt{x+7}\right)^{2}$

Square of the first term: $\left(-\sqrt{x+7}\right)^2 = \left(-\sqrt{x+7}\right)^2$.

Double product of the first by the second: $2\left(-\sqrt{x+7}\right)\left(7\right) = 2\cdot 7\left(-\sqrt{x+7}\right)$.

Square of the second term: $\left(7\right)^2 = 7^2$

4

Expand $\left(7-\sqrt{x+7}\right)^{2}$

$x=56+x-14\sqrt{x+7}$
5

Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side

$x-x+14\sqrt{x+7}=56$
6

Cancel like terms $x$ and $-x$

$14\sqrt{x+7}=56$
7

Divide both sides of the equation by $14$

$\frac{14\sqrt{x+7}}{14}=\frac{56}{14}$
8

Simplifying the quotients

$\sqrt{x+7}=4$
9

Removing the variable's exponent raising both sides of the equation to the power $2$

$x+7=16$
10

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $7$ from both sides of the equation

$x=9$

$x=9$