Solve 640y^2-10=0

$$640 y ^ { 2 } - 10 = 0$$

Solve for y

$$y=\frac{1}{8}=0.125$$

$$y=-\frac{1}{8}=-0.125$$

Steps Using Difference of Squares

Divide both sides by 10.

$$64y^{2}-1=0$$

Consider 64y^{2}-1. Rewrite 64y^{2}-1 as \left(8y\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(8y-1\right)\left(8y+1\right)=0$$

To find equation solutions, solve 8y-1=0 and 8y+1=0.

$$y=\frac{1}{8} y=-\frac{1}{8}$$

Steps by Finding Square Root

Add 10 to both sides. Anything plus zero gives itself.

$$640y^{2}=10$$

Divide both sides by 640.

$$y^{2}=\frac{10}{640}$$

Reduce the fraction \frac{10}{640} to lowest terms by extracting and canceling out 10.

$$y^{2}=\frac{1}{64}$$

Take the square root of both sides of the equation.

$$y=\frac{1}{8} y=-\frac{1}{8}$$

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.

$$640y^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 640 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 640\left(-10\right)}}{2\times 640}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 640\left(-10\right)}}{2\times 640}$$

Multiply -4 times 640.

$$y=\frac{0±\sqrt{-2560\left(-10\right)}}{2\times 640}$$

Multiply -2560 times -10.

$$y=\frac{0±\sqrt{25600}}{2\times 640}$$

Take the square root of 25600.

$$y=\frac{0±160}{2\times 640}$$

Multiply 2 times 640.

$$y=\frac{0±160}{1280}$$

Now solve the equation y=\frac{0±160}{1280} when ± is plus. Reduce the fraction \frac{160}{1280} to lowest terms by extracting and canceling out 160.

$$y=\frac{1}{8}$$

Now solve the equation y=\frac{0±160}{1280} when ± is minus. Reduce the fraction \frac{-160}{1280} to lowest terms by extracting and canceling out 160.

$$y=-\frac{1}{8}$$

The equation is now solved.

$$y=\frac{1}{8} y=-\frac{1}{8}$$