Solve 2x^2+3=5^2+14

$$2 x ^ { 2 } + 3 = 5 ^ { 2 } + 14$$

Solve for x

$$x=3\sqrt{2}\approx 4.242640687$$

$$x=-3\sqrt{2}\approx -4.242640687$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$2x^{2}+3=25+14$$

Add 25 and 14 to get 39.

$$2x^{2}+3=39$$

Subtract 3 from both sides.

$$2x^{2}=39-3$$

Subtract 3 from 39 to get 36.

$$2x^{2}=36$$

Divide both sides by 2.

$$x^{2}=\frac{36}{2}$$

Divide 36 by 2 to get 18.

$$x^{2}=18$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$2x^{2}+3=25+14$$

Add 25 and 14 to get 39.

$$2x^{2}+3=39$$

Subtract 39 from both sides.

$$2x^{2}+3-39=0$$

Subtract 39 from 3 to get -36.

$$2x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-36\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-36\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-36\right)}}{2\times 2}$$

Multiply -8 times -36.

$$x=\frac{0±\sqrt{288}}{2\times 2}$$

Take the square root of 288.

$$x=\frac{0±12\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±12\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±12\sqrt{2}}{4} when ± is plus.

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

Now solve the equation x=\frac{0±12\sqrt{2}}{4} when ± is minus.

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

The equation is now solved.

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