Solve 144x^2+0x-400=0

$$144 { x }^{ 2 } +0x-400=0$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

Steps Using Difference of Squares

Divide both sides by 16.

$$9x^{2}+0-25=0$$

Consider 9x^{2}+0x-25. Rewrite 9x^{2}+0-25 as \left(3x\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).

$$\left(3x-5\right)\left(3x+5\right)=0$$

To find equation solutions, solve 3x-5=0 and 3x+5=0.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Steps by Finding Square Root

Anything times zero gives zero.

$$144x^{2}+0-400=0$$

Subtract 400 from 0 to get -400.

$$144x^{2}-400=0$$

Add 400 to both sides. Anything plus zero gives itself.

$$144x^{2}=400$$

Divide both sides by 144.

$$x^{2}=\frac{400}{144}$$

Reduce the fraction \frac{400}{144} to lowest terms by extracting and canceling out 16.

$$x^{2}=\frac{25}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Steps Using the Quadratic Formula

Anything times zero gives zero.

$$144x^{2}+0-400=0$$

Subtract 400 from 0 to get -400.

$$144x^{2}-400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 144 for a, 0 for b, and -400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 144\left(-400\right)}}{2\times 144}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 144\left(-400\right)}}{2\times 144}$$

Multiply -4 times 144.

$$x=\frac{0±\sqrt{-576\left(-400\right)}}{2\times 144}$$

Multiply -576 times -400.

$$x=\frac{0±\sqrt{230400}}{2\times 144}$$

Take the square root of 230400.

$$x=\frac{0±480}{2\times 144}$$

Multiply 2 times 144.

$$x=\frac{0±480}{288}$$

Now solve the equation x=\frac{0±480}{288} when ± is plus. Reduce the fraction \frac{480}{288} to lowest terms by extracting and canceling out 96.

$$x=\frac{5}{3}$$

Now solve the equation x=\frac{0±480}{288} when ± is minus. Reduce the fraction \frac{-480}{288} to lowest terms by extracting and canceling out 96.

$$x=-\frac{5}{3}$$

The equation is now solved.

$$x=\frac{5}{3} x=-\frac{5}{3}$$