Solve 25/4x^2-1=0

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

Solve for x

$$x=\frac{2}{5}=0.4$$

$$x=-\frac{2}{5}=-0.4$$

Steps Using Difference of Squares

Multiply both sides by 4.

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

Consider 25x^{2}-4. Rewrite 25x^{2}-4 as \left(5x\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).

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

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

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

Steps by Finding Square Root

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

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

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

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

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

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

Take the square root of both sides of the equation.

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

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.

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

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

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

Square 0.

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

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

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

Multiply -25 times -1.

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

Take the square root of 25.

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

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

$$x=\frac{0±5}{\frac{25}{2}}$$

Now solve the equation x=\frac{0±5}{\frac{25}{2}} when ± is plus. Divide 5 by \frac{25}{2} by multiplying 5 by the reciprocal of \frac{25}{2}.

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

Now solve the equation x=\frac{0±5}{\frac{25}{2}} when ± is minus. Divide -5 by \frac{25}{2} by multiplying -5 by the reciprocal of \frac{25}{2}.

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

The equation is now solved.

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