Solve 4/25x^2-1=0

$$\frac{ 4 }{ 25 } { x }^{ 2 } -1=0$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps Using Difference of Squares

Multiply both sides by 25.

$$4x^{2}-25=0$$

Consider 4x^{2}-25. Rewrite 4x^{2}-25 as \left(2x\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).

$$\left(2x-5\right)\left(2x+5\right)=0$$

To find equation solutions, solve 2x-5=0 and 2x+5=0.

$$x=\frac{5}{2} x=-\frac{5}{2}$$

Steps by Finding Square Root

Add 1 to both sides. Anything plus zero gives itself.

$$\frac{4}{25}x^{2}=1$$

Multiply both sides by \frac{25}{4}, the reciprocal of \frac{4}{25}.

$$x^{2}=1\times \frac{25}{4}$$

Multiply 1 and \frac{25}{4} to get \frac{25}{4}.

$$x^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{5}{2} x=-\frac{5}{2}$$

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.

$$\frac{4}{25}x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{4}{25} for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{4}{25}\left(-1\right)}}{2\times \frac{4}{25}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{4}{25}\left(-1\right)}}{2\times \frac{4}{25}}$$

Multiply -4 times \frac{4}{25}.

$$x=\frac{0±\sqrt{-\frac{16}{25}\left(-1\right)}}{2\times \frac{4}{25}}$$

Multiply -\frac{16}{25} times -1.

$$x=\frac{0±\sqrt{\frac{16}{25}}}{2\times \frac{4}{25}}$$

Take the square root of \frac{16}{25}.

$$x=\frac{0±\frac{4}{5}}{2\times \frac{4}{25}}$$

Multiply 2 times \frac{4}{25}.

$$x=\frac{0±\frac{4}{5}}{\frac{8}{25}}$$

Now solve the equation x=\frac{0±\frac{4}{5}}{\frac{8}{25}} when ± is plus.

$$x=\frac{5}{2}$$

Now solve the equation x=\frac{0±\frac{4}{5}}{\frac{8}{25}} when ± is minus.

$$x=-\frac{5}{2}$$

The equation is now solved.

$$x=\frac{5}{2} x=-\frac{5}{2}$$