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Equations with square roots Calculator

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1

Solved example of equations with square roots

$\left(x+2\right)^2=\sqrt{-4}$
2

Calculate the power using complex numbers

$\left(x+2\right)^2=2i$
3

Removing the variable's exponent

$\sqrt{\left(x+2\right)^2}=\pm \sqrt{2i}$
4

Cancel exponents $2$ and $0.5$

$x+2=\pm \sqrt{2i}$
5

As in the equation we have the sign $\pm$, this produces two identical equations that differ in the sign of the term $\sqrt{2i}$. We write and solve both equations, one taking the positive sign, and the other taking the negative sign

$x+2=\sqrt{2i},\:x+2=-1\cdot \sqrt{2i}$
6

Solve the equation ($1$)

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

Subtract $2$ from both sides of the equation

$x=\sqrt{2i}-2$
8

The power of a product is equal to the product of it's factors raised to the same power

$x=\sqrt{2}\cdot \sqrt{i}-2$
9

Solve the equation ($2$)

$x+2=-1\cdot \sqrt{2i}$
10

Subtract $2$ from both sides of the equation

$x=-1\cdot \sqrt{2i}-2$
11

The power of a product is equal to the product of it's factors raised to the same power

$x=-\sqrt{2}\cdot \sqrt{i}-2$
12

The $2$ solutions of the equation are

$x=\sqrt{2}\cdot \sqrt{i}-2,\:x=-\sqrt{2}\cdot \sqrt{i}-2$

Answer

$x=\sqrt{2}\cdot \sqrt{i}-2,\:x=-\sqrt{2}\cdot \sqrt{i}-2$

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