Solve 2x^2-19=9

$$2 x ^ { 2 } - 19 = 9$$

Solve for x

$$x=\sqrt{14}\approx 3.741657387$$

$$x=-\sqrt{14}\approx -3.741657387$$

Steps by Finding Square Root

Add 19 to both sides.

$$2x^{2}=9+19$$

Add 9 and 19 to get 28.

$$2x^{2}=28$$

Divide both sides by 2.

$$x^{2}=\frac{28}{2}$$

Divide 28 by 2 to get 14.

$$x^{2}=14$$

Take the square root of both sides of the equation.

$$x=\sqrt{14} x=-\sqrt{14}$$

Steps Using the Quadratic Formula

Subtract 9 from both sides.

$$2x^{2}-19-9=0$$

Subtract 9 from -19 to get -28.

$$2x^{2}-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-28\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-28\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-28\right)}}{2\times 2}$$

Multiply -8 times -28.

$$x=\frac{0±\sqrt{224}}{2\times 2}$$

Take the square root of 224.

$$x=\frac{0±4\sqrt{14}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{14}}{4}$$

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

$$x=\sqrt{14}$$

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

$$x=-\sqrt{14}$$

The equation is now solved.

$$x=\sqrt{14} x=-\sqrt{14}$$