Solve 20^2=x^2+3x^2

$$20 ^ { 2 } = x ^ { 2 } + 3 x ^ { 2 }$$

Solve for x

$$x=10$$

$$x=-10$$

Steps Using Difference of Squares

Calculate 20 to the power of 2 and get 400.

$$400=x^{2}+3x^{2}$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$400=4x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}=400$$

Subtract 400 from both sides.

$$4x^{2}-400=0$$

Divide both sides by 4.

$$x^{2}-100=0$$

Consider x^{2}-100. Rewrite x^{2}-100 as x^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-10\right)\left(x+10\right)=0$$

To find equation solutions, solve x-10=0 and x+10=0.

$$x=10 x=-10$$

Steps by Finding Square Root

Calculate 20 to the power of 2 and get 400.

$$400=x^{2}+3x^{2}$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$400=4x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}=400$$

Divide both sides by 4.

$$x^{2}=\frac{400}{4}$$

Divide 400 by 4 to get 100.

$$x^{2}=100$$

Take the square root of both sides of the equation.

$$x=10 x=-10$$

Steps Using the Quadratic Formula

Calculate 20 to the power of 2 and get 400.

$$400=x^{2}+3x^{2}$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$400=4x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}=400$$

Subtract 400 from both sides.

$$4x^{2}-400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-400\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-400\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-400\right)}}{2\times 4}$$

Multiply -16 times -400.

$$x=\frac{0±\sqrt{6400}}{2\times 4}$$

Take the square root of 6400.

$$x=\frac{0±80}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±80}{8}$$

Now solve the equation x=\frac{0±80}{8} when ± is plus. Divide 80 by 8.

$$x=10$$

Now solve the equation x=\frac{0±80}{8} when ± is minus. Divide -80 by 8.

$$x=-10$$

The equation is now solved.

$$x=10 x=-10$$