Solve 2x^2-7=38

$$2 x ^ { 2 } - 7 = 38$$

Solve for x

$$x = \frac{3 \sqrt{10}}{2} \approx 4.74341649$$

$$x = -\frac{3 \sqrt{10}}{2} \approx -4.74341649$$

Steps by Finding Square Root

Add 7 to both sides.

$$2x^{2}=38+7$$

Add 38 and 7 to get 45.

$$2x^{2}=45$$

Divide both sides by 2.

$$x^{2}=\frac{45}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{10}}{2} x=-\frac{3\sqrt{10}}{2}$$

Steps Using the Quadratic Formula

Subtract 38 from both sides.

$$2x^{2}-7-38=0$$

Subtract 38 from -7 to get -45.

$$2x^{2}-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-45\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-45\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-45\right)}}{2\times 2}$$

Multiply -8 times -45.

$$x=\frac{0±\sqrt{360}}{2\times 2}$$

Take the square root of 360.

$$x=\frac{0±6\sqrt{10}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±6\sqrt{10}}{4}$$

Now solve the equation x=\frac{0±6\sqrt{10}}{4} when ± is plus.

$$x=\frac{3\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{10}}{4} when ± is minus.

$$x=-\frac{3\sqrt{10}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{10}}{2} x=-\frac{3\sqrt{10}}{2}$$