Solve 2x^2-40=9

$$2 x ^ { 2 } - 40 = 9$$

Solve for x

$$x = \frac{7 \sqrt{2}}{2} \approx 4.949747468$$

$$x = -\frac{7 \sqrt{2}}{2} \approx -4.949747468$$

Steps by Finding Square Root

Add 40 to both sides.

$$2x^{2}=9+40$$

Add 9 and 40 to get 49.

$$2x^{2}=49$$

Divide both sides by 2.

$$x^{2}=\frac{49}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{7\sqrt{2}}{2} x=-\frac{7\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Subtract 9 from both sides.

$$2x^{2}-40-9=0$$

Subtract 9 from -40 to get -49.

$$2x^{2}-49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-49\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-49\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-49\right)}}{2\times 2}$$

Multiply -8 times -49.

$$x=\frac{0±\sqrt{392}}{2\times 2}$$

Take the square root of 392.

$$x=\frac{0±14\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±14\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±14\sqrt{2}}{4} when ± is plus.

$$x=\frac{7\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±14\sqrt{2}}{4} when ± is minus.

$$x=-\frac{7\sqrt{2}}{2}$$

The equation is now solved.

$$x=\frac{7\sqrt{2}}{2} x=-\frac{7\sqrt{2}}{2}$$