Solve a^2+7=43

$$a ^ { 2 } + 7 = 43$$

Solve for a

$$a=6$$

$$a=-6$$

Steps Using Difference of Squares

Subtract 43 from both sides.

$$a^{2}+7-43=0$$

Subtract 43 from 7 to get -36.

$$a^{2}-36=0$$

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

$$\left(a-6\right)\left(a+6\right)=0$$

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

$$a=6 a=-6$$

Steps by Finding Square Root

Subtract 7 from both sides.

$$a^{2}=43-7$$

Subtract 7 from 43 to get 36.

$$a^{2}=36$$

Take the square root of both sides of the equation.

$$a=6 a=-6$$

Steps Using the Quadratic Formula

Subtract 43 from both sides.

$$a^{2}+7-43=0$$

Subtract 43 from 7 to get -36.

$$a^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -36.

$$a=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$a=\frac{0±12}{2}$$

Now solve the equation a=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$a=6$$

Now solve the equation a=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$a=-6$$

The equation is now solved.

$$a=6 a=-6$$