Solve x^2+2x-3=-x^2+2x+30

$$x ^ { 2 } + 2 x - 3 = - x ^ { 2 } + 2 x + 30$$

Solve for x

$$x = \frac{\sqrt{66}}{2} \approx 4.062019202$$

$$x = -\frac{\sqrt{66}}{2} \approx -4.062019202$$

Steps by Finding Square Root

Add x^{2} to both sides.

$$x^{2}+2x-3+x^{2}=2x+30$$

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

$$2x^{2}+2x-3=2x+30$$

Subtract 2x from both sides.

$$2x^{2}+2x-3-2x=30$$

Combine 2x and -2x to get 0.

$$2x^{2}-3=30$$

Add 3 to both sides.

$$2x^{2}=30+3$$

Add 30 and 3 to get 33.

$$2x^{2}=33$$

Divide both sides by 2.

$$x^{2}=\frac{33}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{66}}{2} x=-\frac{\sqrt{66}}{2}$$

Steps Using the Quadratic Formula

Add x^{2} to both sides.

$$x^{2}+2x-3+x^{2}=2x+30$$

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

$$2x^{2}+2x-3=2x+30$$

Subtract 2x from both sides.

$$2x^{2}+2x-3-2x=30$$

Combine 2x and -2x to get 0.

$$2x^{2}-3=30$$

Subtract 30 from both sides.

$$2x^{2}-3-30=0$$

Subtract 30 from -3 to get -33.

$$2x^{2}-33=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -33 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-33\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-33\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-33\right)}}{2\times 2}$$

Multiply -8 times -33.

$$x=\frac{0±\sqrt{264}}{2\times 2}$$

Take the square root of 264.

$$x=\frac{0±2\sqrt{66}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{66}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{66}}{4} when ± is plus.

$$x=\frac{\sqrt{66}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{66}}{4} when ± is minus.

$$x=-\frac{\sqrt{66}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{66}}{2} x=-\frac{\sqrt{66}}{2}$$