Solve 2(x^2-4)+3=15

$$2 ( x ^ { 2 } - 4 ) + 3 = 15$$

Solve for x

$$x=\sqrt{10}\approx 3.16227766$$

$$x=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

Use the distributive property to multiply 2 by x^{2}-4.

$$2x^{2}-8+3=15$$

Add -8 and 3 to get -5.

$$2x^{2}-5=15$$

Add 5 to both sides.

$$2x^{2}=15+5$$

Add 15 and 5 to get 20.

$$2x^{2}=20$$

Divide both sides by 2.

$$x^{2}=\frac{20}{2}$$

Divide 20 by 2 to get 10.

$$x^{2}=10$$

Take the square root of both sides of the equation.

$$x=\sqrt{10} x=-\sqrt{10}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2 by x^{2}-4.

$$2x^{2}-8+3=15$$

Add -8 and 3 to get -5.

$$2x^{2}-5=15$$

Subtract 15 from both sides.

$$2x^{2}-5-15=0$$

Subtract 15 from -5 to get -20.

$$2x^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-20\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-20\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-20\right)}}{2\times 2}$$

Multiply -8 times -20.

$$x=\frac{0±\sqrt{160}}{2\times 2}$$

Take the square root of 160.

$$x=\frac{0±4\sqrt{10}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{10}}{4}$$

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

$$x=\sqrt{10}$$

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

$$x=-\sqrt{10}$$

The equation is now solved.

$$x=\sqrt{10} x=-\sqrt{10}$$