Solve 70-5x^2=40

$$70 - 5 x ^ { 2 } = 40$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Subtract 70 from both sides.

$$-5x^{2}=40-70$$

Subtract 70 from 40 to get -30.

$$-5x^{2}=-30$$

Divide both sides by -5.

$$x^{2}=\frac{-30}{-5}$$

Divide -30 by -5 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

Subtract 40 from both sides.

$$70-5x^{2}-40=0$$

Subtract 40 from 70 to get 30.

$$30-5x^{2}=0$$

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.

$$-5x^{2}+30=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and 30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 30}}{2\left(-5\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\times 30}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20\times 30}}{2\left(-5\right)}$$

Multiply 20 times 30.

$$x=\frac{0±\sqrt{600}}{2\left(-5\right)}$$

Take the square root of 600.

$$x=\frac{0±10\sqrt{6}}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{0±10\sqrt{6}}{-10}$$

Now solve the equation x=\frac{0±10\sqrt{6}}{-10} when ± is plus.

$$x=-\sqrt{6}$$

Now solve the equation x=\frac{0±10\sqrt{6}}{-10} when ± is minus.

$$x=\sqrt{6}$$

The equation is now solved.

$$x=-\sqrt{6} x=\sqrt{6}$$