Solve j^2-64=-15

$$j ^ { 2 } - 64 = - 15$$

Solve for j

$$j=7$$

$$j=-7$$

Steps Using Difference of Squares

Add 15 to both sides.

$$j^{2}-64+15=0$$

Add -64 and 15 to get -49.

$$j^{2}-49=0$$

Consider j^{2}-49. Rewrite j^{2}-49 as j^{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).

$$\left(j-7\right)\left(j+7\right)=0$$

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

$$j=7 j=-7$$

Steps by Finding Square Root

Add 64 to both sides.

$$j^{2}=-15+64$$

Add -15 and 64 to get 49.

$$j^{2}=49$$

Take the square root of both sides of the equation.

$$j=7 j=-7$$

Steps Using the Quadratic Formula

Add 15 to both sides.

$$j^{2}-64+15=0$$

Add -64 and 15 to get -49.

$$j^{2}-49=0$$

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

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

Square 0.

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

Multiply -4 times -49.

$$j=\frac{0±\sqrt{196}}{2}$$

Take the square root of 196.

$$j=\frac{0±14}{2}$$

Now solve the equation j=\frac{0±14}{2} when ± is plus. Divide 14 by 2.

$$j=7$$

Now solve the equation j=\frac{0±14}{2} when ± is minus. Divide -14 by 2.

$$j=-7$$

The equation is now solved.

$$j=7 j=-7$$