Solve 7-2x^2=-47

$$7-2 { x }^{ 2 } =-47$$

Solve for x

$$x=3\sqrt{3}\approx 5.196152423$$

$$x=-3\sqrt{3}\approx -5.196152423$$

Steps by Finding Square Root

Subtract 7 from both sides.

$$-2x^{2}=-47-7$$

Subtract 7 from -47 to get -54.

$$-2x^{2}=-54$$

Divide both sides by -2.

$$x^{2}=\frac{-54}{-2}$$

Divide -54 by -2 to get 27.

$$x^{2}=27$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Add 47 to both sides.

$$7-2x^{2}+47=0$$

Add 7 and 47 to get 54.

$$54-2x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-2x^{2}+54=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 54 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 54}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 54}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 54}}{2\left(-2\right)}$$

Multiply 8 times 54.

$$x=\frac{0±\sqrt{432}}{2\left(-2\right)}$$

Take the square root of 432.

$$x=\frac{0±12\sqrt{3}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±12\sqrt{3}}{-4}$$

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

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

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

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

The equation is now solved.

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