Solve (1-m)^2/2=5-m

$$\frac { ( 1 - m ) ^ { 2 } } { 2 } = 5 - m$$

Solve for m

$$m=3$$

$$m=-3$$

Steps Using Difference of Squares

Multiply both sides of the equation by 2.

$$\left(1-m\right)^{2}=10-2m$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-m\right)^{2}.

$$1-2m+m^{2}=10-2m$$

Subtract 10 from both sides.

$$1-2m+m^{2}-10=-2m$$

Subtract 10 from 1 to get -9.

$$-9-2m+m^{2}=-2m$$

Add 2m to both sides.

$$-9-2m+m^{2}+2m=0$$

Combine -2m and 2m to get 0.

$$-9+m^{2}=0$$

Consider -9+m^{2}. Rewrite -9+m^{2} as m^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m-3\right)\left(m+3\right)=0$$

To find equation solutions, solve m-3=0 and m+3=0.

$$m=3 m=-3$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$\left(1-m\right)^{2}=10-2m$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-m\right)^{2}.

$$1-2m+m^{2}=10-2m$$

Add 2m to both sides.

$$1-2m+m^{2}+2m=10$$

Combine -2m and 2m to get 0.

$$1+m^{2}=10$$

Subtract 1 from both sides.

$$m^{2}=10-1$$

Subtract 1 from 10 to get 9.

$$m^{2}=9$$

Take the square root of both sides of the equation.

$$m=3 m=-3$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$\left(1-m\right)^{2}=10-2m$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-m\right)^{2}.

$$1-2m+m^{2}=10-2m$$

Subtract 10 from both sides.

$$1-2m+m^{2}-10=-2m$$

Subtract 10 from 1 to get -9.

$$-9-2m+m^{2}=-2m$$

Add 2m to both sides.

$$-9-2m+m^{2}+2m=0$$

Combine -2m and 2m to get 0.

$$-9+m^{2}=0$$

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.

$$m^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-9\right)}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-9\right)}}{2}$$

Multiply -4 times -9.

$$m=\frac{0±\sqrt{36}}{2}$$

Take the square root of 36.

$$m=\frac{0±6}{2}$$

Now solve the equation m=\frac{0±6}{2} when ± is plus. Divide 6 by 2.

$$m=3$$

Now solve the equation m=\frac{0±6}{2} when ± is minus. Divide -6 by 2.

$$m=-3$$

The equation is now solved.

$$m=3 m=-3$$