Solve 2x^2-43=x^2

$$2 x ^ { 2 } - 43 = x ^ { 2 }$$

Solve for x

$$x=\sqrt{43}\approx 6.557438524$$

$$x=-\sqrt{43}\approx -6.557438524$$

Steps by Finding Square Root

Subtract x^{2} from both sides.

$$2x^{2}-43-x^{2}=0$$

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

$$x^{2}-43=0$$

Add 43 to both sides. Anything plus zero gives itself.

$$x^{2}=43$$

Take the square root of both sides of the equation.

$$x=\sqrt{43} x=-\sqrt{43}$$

Steps Using the Quadratic Formula

Subtract x^{2} from both sides.

$$2x^{2}-43-x^{2}=0$$

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

$$x^{2}-43=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -43 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-43\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-43\right)}}{2}$$

Multiply -4 times -43.

$$x=\frac{0±\sqrt{172}}{2}$$

Take the square root of 172.

$$x=\frac{0±2\sqrt{43}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{43}}{2} when ± is plus.

$$x=\sqrt{43}$$

Now solve the equation x=\frac{0±2\sqrt{43}}{2} when ± is minus.

$$x=-\sqrt{43}$$

The equation is now solved.

$$x=\sqrt{43} x=-\sqrt{43}$$