Solve (2x)^2-2x(-x)-3=-1

$$( 2 x ) ^ { 2 } - 2 x ( - x ) - 3 = - 1$$

Solve for x

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps by Finding Square Root

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

$$2^{2}x^{2}-2x\left(-x\right)-3=-1$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-2x\left(-x\right)-3=-1$$

Add 3 to both sides.

$$4x^{2}-2x\left(-x\right)=-1+3$$

Add -1 and 3 to get 2.

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

Multiply x and x to get x^{2}.

$$4x^{2}-2x^{2}\left(-1\right)=2$$

Multiply -2 and -1 to get 2.

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

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}=2$$

Divide both sides by 6.

$$x^{2}=\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{1}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3}}{3} x=-\frac{\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

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

$$2^{2}x^{2}-2x\left(-x\right)-3=-1$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-2x\left(-x\right)-3=-1$$

Add 1 to both sides.

$$4x^{2}-2x\left(-x\right)-3+1=0$$

Add -3 and 1 to get -2.

$$4x^{2}-2x\left(-x\right)-2=0$$

Multiply x and x to get x^{2}.

$$4x^{2}-2x^{2}\left(-1\right)-2=0$$

Multiply -2 and -1 to get 2.

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

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-2\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-2\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-2\right)}}{2\times 6}$$

Multiply -24 times -2.

$$x=\frac{0±\sqrt{48}}{2\times 6}$$

Take the square root of 48.

$$x=\frac{0±4\sqrt{3}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±4\sqrt{3}}{12}$$

Now solve the equation x=\frac{0±4\sqrt{3}}{12} when ± is plus.

$$x=\frac{\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{3}}{12} when ± is minus.

$$x=-\frac{\sqrt{3}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{3}}{3} x=-\frac{\sqrt{3}}{3}$$