Solve 49y^2=1

$$49 y ^ { 2 } = 1$$

Solve for y

$$y=\frac{1}{7}\approx 0.142857143$$

$$y=-\frac{1}{7}\approx -0.142857143$$

Steps Using Difference of Squares

Divide both sides by 49.

$$y^{2}=\frac{1}{49}$$

Subtract \frac{1}{49} from both sides.

$$y^{2}-\frac{1}{49}=0$$

Multiply both sides by 49.

$$49y^{2}-1=0$$

Consider 49y^{2}-1. Rewrite 49y^{2}-1 as \left(7y\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).

$$\left(7y-1\right)\left(7y+1\right)=0$$

To find equation solutions, solve 7y-1=0 and 7y+1=0.

$$y=\frac{1}{7} y=-\frac{1}{7}$$

Steps by Finding Square Root

Divide both sides by 49.

$$y^{2}=\frac{1}{49}$$

Take the square root of both sides of the equation.

$$y=\frac{1}{7} y=-\frac{1}{7}$$

Steps Using the Quadratic Formula

Divide both sides by 49.

$$y^{2}=\frac{1}{49}$$

Subtract \frac{1}{49} from both sides.

$$y^{2}-\frac{1}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{49}\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{1}{49}\right)}}{2}$$

Multiply -4 times -\frac{1}{49}.

$$y=\frac{0±\sqrt{\frac{4}{49}}}{2}$$

Take the square root of \frac{4}{49}.

$$y=\frac{0±\frac{2}{7}}{2}$$

Now solve the equation y=\frac{0±\frac{2}{7}}{2} when ± is plus.

$$y=\frac{1}{7}$$

Now solve the equation y=\frac{0±\frac{2}{7}}{2} when ± is minus.

$$y=-\frac{1}{7}$$

The equation is now solved.

$$y=\frac{1}{7} y=-\frac{1}{7}$$