Solve 72x^2+67=99

$$72 { x }^{ 2 } +67=99$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

$$x=-\frac{2}{3}\approx -0.666666667$$

Steps Using Difference of Squares

Subtract 99 from both sides.

$$72x^{2}+67-99=0$$

Subtract 99 from 67 to get -32.

$$72x^{2}-32=0$$

Divide both sides by 8.

$$9x^{2}-4=0$$

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

$$\left(3x-2\right)\left(3x+2\right)=0$$

To find equation solutions, solve 3x-2=0 and 3x+2=0.

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

Steps by Finding Square Root

Subtract 67 from both sides.

$$72x^{2}=99-67$$

Subtract 67 from 99 to get 32.

$$72x^{2}=32$$

Divide both sides by 72.

$$x^{2}=\frac{32}{72}$$

Reduce the fraction \frac{32}{72} to lowest terms by extracting and canceling out 8.

$$x^{2}=\frac{4}{9}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 99 from both sides.

$$72x^{2}+67-99=0$$

Subtract 99 from 67 to get -32.

$$72x^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 72 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 72\left(-32\right)}}{2\times 72}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 72\left(-32\right)}}{2\times 72}$$

Multiply -4 times 72.

$$x=\frac{0±\sqrt{-288\left(-32\right)}}{2\times 72}$$

Multiply -288 times -32.

$$x=\frac{0±\sqrt{9216}}{2\times 72}$$

Take the square root of 9216.

$$x=\frac{0±96}{2\times 72}$$

Multiply 2 times 72.

$$x=\frac{0±96}{144}$$

Now solve the equation x=\frac{0±96}{144} when ± is plus. Reduce the fraction \frac{96}{144} to lowest terms by extracting and canceling out 48.

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

Now solve the equation x=\frac{0±96}{144} when ± is minus. Reduce the fraction \frac{-96}{144} to lowest terms by extracting and canceling out 48.

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

The equation is now solved.

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