Solve m^2+10m+25+4-2m=0

$$m ^ { 2 } + 10 m + 25 + 4 - 2 m = 0$$

Solve for m

$$m=-4+\sqrt{13}i\approx -4+3.605551275i$$

$$m=-\sqrt{13}i-4\approx -4-3.605551275i$$

Steps Using the Quadratic Formula

Add 25 and 4 to get 29.

$$m^{2}+10m+29-2m=0$$

Combine 10m and -2m to get 8m.

$$m^{2}+8m+29=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and 29 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-8±\sqrt{8^{2}-4\times 29}}{2}$$

Square 8.

$$m=\frac{-8±\sqrt{64-4\times 29}}{2}$$

Multiply -4 times 29.

$$m=\frac{-8±\sqrt{64-116}}{2}$$

Add 64 to -116.

$$m=\frac{-8±\sqrt{-52}}{2}$$

Take the square root of -52.

$$m=\frac{-8±2\sqrt{13}i}{2}$$

Now solve the equation m=\frac{-8±2\sqrt{13}i}{2} when ± is plus. Add -8 to 2i\sqrt{13}.

$$m=\frac{-8+2\sqrt{13}i}{2}$$

Divide -8+2i\sqrt{13} by 2.

$$m=-4+\sqrt{13}i$$

Now solve the equation m=\frac{-8±2\sqrt{13}i}{2} when ± is minus. Subtract 2i\sqrt{13} from -8.

$$m=\frac{-2\sqrt{13}i-8}{2}$$

Divide -8-2i\sqrt{13} by 2.

$$m=-\sqrt{13}i-4$$

The equation is now solved.

$$m=-4+\sqrt{13}i m=-\sqrt{13}i-4$$

Steps for Completing the Square

Add 25 and 4 to get 29.

$$m^{2}+10m+29-2m=0$$

Combine 10m and -2m to get 8m.

$$m^{2}+8m+29=0$$

Subtract 29 from both sides. Anything subtracted from zero gives its negation.

$$m^{2}+8m=-29$$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}+8m+4^{2}=-29+4^{2}$$

Square 4.

$$m^{2}+8m+16=-29+16$$

Add -29 to 16.

$$m^{2}+8m+16=-13$$

Factor m^{2}+8m+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m+4\right)^{2}=-13$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m+4\right)^{2}}=\sqrt{-13}$$

Simplify.

$$m+4=\sqrt{13}i m+4=-\sqrt{13}i$$

Subtract 4 from both sides of the equation.

$$m=-4+\sqrt{13}i m=-\sqrt{13}i-4$$