Solve 36x^2+5=14

$$36 x ^ { 2 } + 5 = 14$$

Solve for x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Steps Using Difference of Squares

Subtract 14 from both sides.

$$36x^{2}+5-14=0$$

Subtract 14 from 5 to get -9.

$$36x^{2}-9=0$$

Divide both sides by 9.

$$4x^{2}-1=0$$

Consider 4x^{2}-1. Rewrite 4x^{2}-1 as \left(2x\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-1\right)\left(2x+1\right)=0$$

To find equation solutions, solve 2x-1=0 and 2x+1=0.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Steps by Finding Square Root

Subtract 5 from both sides.

$$36x^{2}=14-5$$

Subtract 5 from 14 to get 9.

$$36x^{2}=9$$

Divide both sides by 36.

$$x^{2}=\frac{9}{36}$$

Reduce the fraction \frac{9}{36} to lowest terms by extracting and canceling out 9.

$$x^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

Steps Using the Quadratic Formula

Subtract 14 from both sides.

$$36x^{2}+5-14=0$$

Subtract 14 from 5 to get -9.

$$36x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 36\left(-9\right)}}{2\times 36}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 36\left(-9\right)}}{2\times 36}$$

Multiply -4 times 36.

$$x=\frac{0±\sqrt{-144\left(-9\right)}}{2\times 36}$$

Multiply -144 times -9.

$$x=\frac{0±\sqrt{1296}}{2\times 36}$$

Take the square root of 1296.

$$x=\frac{0±36}{2\times 36}$$

Multiply 2 times 36.

$$x=\frac{0±36}{72}$$

Now solve the equation x=\frac{0±36}{72} when ± is plus. Reduce the fraction \frac{36}{72} to lowest terms by extracting and canceling out 36.

$$x=\frac{1}{2}$$

Now solve the equation x=\frac{0±36}{72} when ± is minus. Reduce the fraction \frac{-36}{72} to lowest terms by extracting and canceling out 36.

$$x=-\frac{1}{2}$$

The equation is now solved.

$$x=\frac{1}{2} x=-\frac{1}{2}$$