Solve (m-2)^2-4*1*(m+1)=0

$$( m - 2 ) ^ { 2 } - 4 \times 1 \times ( m + 1 ) = 0$$

Solve for m

$$m=8$$

$$m=0$$

Steps Using Factoring

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

$$m^{2}-4m+4-4\times 1\left(m+1\right)=0$$

Multiply 4 and 1 to get 4.

$$m^{2}-4m+4-4\left(m+1\right)=0$$

Use the distributive property to multiply -4 by m+1.

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

Combine -4m and -4m to get -8m.

$$m^{2}-8m+4-4=0$$

Subtract 4 from 4 to get 0.

$$m^{2}-8m=0$$

Factor out m.

$$m\left(m-8\right)=0$$

To find equation solutions, solve m=0 and m-8=0.

$$m=0 m=8$$

Steps Using the Quadratic Formula

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

$$m^{2}-4m+4-4\times 1\left(m+1\right)=0$$

Multiply 4 and 1 to get 4.

$$m^{2}-4m+4-4\left(m+1\right)=0$$

Use the distributive property to multiply -4 by m+1.

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

Combine -4m and -4m to get -8m.

$$m^{2}-8m+4-4=0$$

Subtract 4 from 4 to get 0.

$$m^{2}-8m=0$$

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

$$m=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2}$$

Take the square root of \left(-8\right)^{2}.

$$m=\frac{-\left(-8\right)±8}{2}$$

The opposite of -8 is 8.

$$m=\frac{8±8}{2}$$

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

$$m=\frac{16}{2}$$

Divide 16 by 2.

$$m=8$$

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

$$m=\frac{0}{2}$$

Divide 0 by 2.

$$m=0$$

The equation is now solved.

$$m=8 m=0$$

Steps for Completing the Square

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

$$m^{2}-4m+4-4\times 1\left(m+1\right)=0$$

Multiply 4 and 1 to get 4.

$$m^{2}-4m+4-4\left(m+1\right)=0$$

Use the distributive property to multiply -4 by m+1.

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

Combine -4m and -4m to get -8m.

$$m^{2}-8m+4-4=0$$

Subtract 4 from 4 to get 0.

$$m^{2}-8m=0$$

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.

$$m^{2}-8m+\left(-4\right)^{2}=\left(-4\right)^{2}$$

Square -4.

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

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}.

$$\left(m-4\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-4\right)^{2}}=\sqrt{16}$$

Simplify.

$$m-4=4 m-4=-4$$

Add 4 to both sides of the equation.

$$m=8 m=0$$