Solve 70-2x^2/4=5

$$\frac { 70 - 2 x ^ { 2 } } { 4 } = 5$$

Solve for x

$$x=5$$

$$x=-5$$

Steps by Finding Square Root

Multiply both sides by 4.

$$70-2x^{2}=5\times 4$$

Multiply 5 and 4 to get 20.

$$70-2x^{2}=20$$

Subtract 70 from both sides.

$$-2x^{2}=20-70$$

Subtract 70 from 20 to get -50.

$$-2x^{2}=-50$$

Divide both sides by -2.

$$x^{2}=\frac{-50}{-2}$$

Divide -50 by -2 to get 25.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

Multiply both sides by 4.

$$70-2x^{2}=5\times 4$$

Multiply 5 and 4 to get 20.

$$70-2x^{2}=20$$

Subtract 20 from both sides.

$$70-2x^{2}-20=0$$

Subtract 20 from 70 to get 50.

$$50-2x^{2}=0$$

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.

$$-2x^{2}+50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 50}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 50}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 50}}{2\left(-2\right)}$$

Multiply 8 times 50.

$$x=\frac{0±\sqrt{400}}{2\left(-2\right)}$$

Take the square root of 400.

$$x=\frac{0±20}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±20}{-4}$$

Now solve the equation x=\frac{0±20}{-4} when ± is plus. Divide 20 by -4.

$$x=-5$$

Now solve the equation x=\frac{0±20}{-4} when ± is minus. Divide -20 by -4.

$$x=5$$

The equation is now solved.

$$x=-5 x=5$$