Solve 16x^2-9=0

$$16 { x }^{ 2 } -9=0$$

Solve for x

$$x=\frac{3}{4}=0.75$$

$$x=-\frac{3}{4}=-0.75$$

Steps Using Difference of Squares

Consider 16x^{2}-9. Rewrite 16x^{2}-9 as \left(4x\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4x-3\right)\left(4x+3\right)=0$$

To find equation solutions, solve 4x-3=0 and 4x+3=0.

$$x=\frac{3}{4} x=-\frac{3}{4}$$

Steps by Finding Square Root

Add 9 to both sides. Anything plus zero gives itself.

$$16x^{2}=9$$

Divide both sides by 16.

$$x^{2}=\frac{9}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{3}{4} x=-\frac{3}{4}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$16x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-9\right)}}{2\times 16}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-9\right)}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\left(-9\right)}}{2\times 16}$$

Multiply -64 times -9.

$$x=\frac{0±\sqrt{576}}{2\times 16}$$

Take the square root of 576.

$$x=\frac{0±24}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±24}{32}$$

Now solve the equation x=\frac{0±24}{32} when ± is plus. Reduce the fraction \frac{24}{32} to lowest terms by extracting and canceling out 8.

$$x=\frac{3}{4}$$

Now solve the equation x=\frac{0±24}{32} when ± is minus. Reduce the fraction \frac{-24}{32} to lowest terms by extracting and canceling out 8.

$$x=-\frac{3}{4}$$

The equation is now solved.

$$x=\frac{3}{4} x=-\frac{3}{4}$$