Solve 72x^2-50=0

$$72 { x }^{ 2 } -50=0$$

Solve for x

$$x=\frac{5}{6}\approx 0.833333333$$

$$x=-\frac{5}{6}\approx -0.833333333$$

Steps Using Difference of Squares

Divide both sides by 2.

$$36x^{2}-25=0$$

Consider 36x^{2}-25. Rewrite 36x^{2}-25 as \left(6x\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(6x-5\right)\left(6x+5\right)=0$$

To find equation solutions, solve 6x-5=0 and 6x+5=0.

$$x=\frac{5}{6} x=-\frac{5}{6}$$

Steps by Finding Square Root

Add 50 to both sides. Anything plus zero gives itself.

$$72x^{2}=50$$

Divide both sides by 72.

$$x^{2}=\frac{50}{72}$$

Reduce the fraction \frac{50}{72} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{25}{36}$$

Take the square root of both sides of the equation.

$$x=\frac{5}{6} x=-\frac{5}{6}$$

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.

$$72x^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 72 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 72\left(-50\right)}}{2\times 72}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 72\left(-50\right)}}{2\times 72}$$

Multiply -4 times 72.

$$x=\frac{0±\sqrt{-288\left(-50\right)}}{2\times 72}$$

Multiply -288 times -50.

$$x=\frac{0±\sqrt{14400}}{2\times 72}$$

Take the square root of 14400.

$$x=\frac{0±120}{2\times 72}$$

Multiply 2 times 72.

$$x=\frac{0±120}{144}$$

Now solve the equation x=\frac{0±120}{144} when ± is plus. Reduce the fraction \frac{120}{144} to lowest terms by extracting and canceling out 24.

$$x=\frac{5}{6}$$

Now solve the equation x=\frac{0±120}{144} when ± is minus. Reduce the fraction \frac{-120}{144} to lowest terms by extracting and canceling out 24.

$$x=-\frac{5}{6}$$

The equation is now solved.

$$x=\frac{5}{6} x=-\frac{5}{6}$$