Solve 8x^2+9=313

$$8 x ^ { 2 } + 9 = 313$$

Solve for x

$$x=\sqrt{38}\approx 6.164414003$$

$$x=-\sqrt{38}\approx -6.164414003$$

Steps by Finding Square Root

Subtract 9 from both sides.

$$8x^{2}=313-9$$

Subtract 9 from 313 to get 304.

$$8x^{2}=304$$

Divide both sides by 8.

$$x^{2}=\frac{304}{8}$$

Divide 304 by 8 to get 38.

$$x^{2}=38$$

Take the square root of both sides of the equation.

$$x=\sqrt{38} x=-\sqrt{38}$$

Steps Using the Quadratic Formula

Subtract 313 from both sides.

$$8x^{2}+9-313=0$$

Subtract 313 from 9 to get -304.

$$8x^{2}-304=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -304 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-304\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-304\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-304\right)}}{2\times 8}$$

Multiply -32 times -304.

$$x=\frac{0±\sqrt{9728}}{2\times 8}$$

Take the square root of 9728.

$$x=\frac{0±16\sqrt{38}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±16\sqrt{38}}{16}$$

Now solve the equation x=\frac{0±16\sqrt{38}}{16} when ± is plus.

$$x=\sqrt{38}$$

Now solve the equation x=\frac{0±16\sqrt{38}}{16} when ± is minus.

$$x=-\sqrt{38}$$

The equation is now solved.

$$x=\sqrt{38} x=-\sqrt{38}$$