Solve 36y^2-49=0

$$36 y ^ { 2 } - 49 = 0$$

Solve for y

$$y = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

$$y = -\frac{7}{6} = -1\frac{1}{6} \approx -1.166666667$$

Steps Using Difference of Squares

Consider 36y^{2}-49. Rewrite 36y^{2}-49 as \left(6y\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(6y-7\right)\left(6y+7\right)=0$$

To find equation solutions, solve 6y-7=0 and 6y+7=0.

$$y=\frac{7}{6} y=-\frac{7}{6}$$

Steps by Finding Square Root

Add 49 to both sides. Anything plus zero gives itself.

$$36y^{2}=49$$

Divide both sides by 36.

$$y^{2}=\frac{49}{36}$$

Take the square root of both sides of the equation.

$$y=\frac{7}{6} y=-\frac{7}{6}$$

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.

$$36y^{2}-49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 36\left(-49\right)}}{2\times 36}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 36\left(-49\right)}}{2\times 36}$$

Multiply -4 times 36.

$$y=\frac{0±\sqrt{-144\left(-49\right)}}{2\times 36}$$

Multiply -144 times -49.

$$y=\frac{0±\sqrt{7056}}{2\times 36}$$

Take the square root of 7056.

$$y=\frac{0±84}{2\times 36}$$

Multiply 2 times 36.

$$y=\frac{0±84}{72}$$

Now solve the equation y=\frac{0±84}{72} when ± is plus. Reduce the fraction \frac{84}{72} to lowest terms by extracting and canceling out 12.

$$y=\frac{7}{6}$$

Now solve the equation y=\frac{0±84}{72} when ± is minus. Reduce the fraction \frac{-84}{72} to lowest terms by extracting and canceling out 12.

$$y=-\frac{7}{6}$$

The equation is now solved.

$$y=\frac{7}{6} y=-\frac{7}{6}$$