Solve x^2+(3x)^2=(sqrt{10})^2

$$x ^ { 2 } + ( 3 x ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$$

Solve for x

$$x=-1$$

$$x=1$$

Steps Using Difference of Squares

Expand \left(3x\right)^{2}.

$$x^{2}+3^{2}x^{2}=\left(\sqrt{10}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+9x^{2}=\left(\sqrt{10}\right)^{2}$$

Combine x^{2} and 9x^{2} to get 10x^{2}.

$$10x^{2}=\left(\sqrt{10}\right)^{2}$$

The square of \sqrt{10} is 10.

$$10x^{2}=10$$

Subtract 10 from both sides.

$$10x^{2}-10=0$$

Divide both sides by 10.

$$x^{2}-1=0$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)=0$$

To find equation solutions, solve x-1=0 and x+1=0.

$$x=1 x=-1$$

Steps by Finding Square Root

Expand \left(3x\right)^{2}.

$$x^{2}+3^{2}x^{2}=\left(\sqrt{10}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+9x^{2}=\left(\sqrt{10}\right)^{2}$$

Combine x^{2} and 9x^{2} to get 10x^{2}.

$$10x^{2}=\left(\sqrt{10}\right)^{2}$$

The square of \sqrt{10} is 10.

$$10x^{2}=10$$

Divide both sides by 10.

$$x^{2}=\frac{10}{10}$$

Divide 10 by 10 to get 1.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

Steps Using the Quadratic Formula

Expand \left(3x\right)^{2}.

$$x^{2}+3^{2}x^{2}=\left(\sqrt{10}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+9x^{2}=\left(\sqrt{10}\right)^{2}$$

Combine x^{2} and 9x^{2} to get 10x^{2}.

$$10x^{2}=\left(\sqrt{10}\right)^{2}$$

The square of \sqrt{10} is 10.

$$10x^{2}=10$$

Subtract 10 from both sides.

$$10x^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10\left(-10\right)}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10\left(-10\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40\left(-10\right)}}{2\times 10}$$

Multiply -40 times -10.

$$x=\frac{0±\sqrt{400}}{2\times 10}$$

Take the square root of 400.

$$x=\frac{0±20}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±20}{20}$$

Now solve the equation x=\frac{0±20}{20} when ± is plus. Divide 20 by 20.

$$x=1$$

Now solve the equation x=\frac{0±20}{20} when ± is minus. Divide -20 by 20.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$