Solve -3.75=(x+1)^2-4

$$- 3.75 = ( x + 1 ) ^ { 2 } - 4$$

Solve for x

$$x=-0.5$$

$$x=-1.5$$

Steps Using the Quadratic Formula

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

$$-3.75=x^{2}+2x+1-4$$

Subtract 4 from 1 to get -3.

$$-3.75=x^{2}+2x-3$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+2x-3=-3.75$$

Add 3.75 to both sides.

$$x^{2}+2x-3+3.75=0$$

Add -3 and 3.75 to get 0.75.

$$x^{2}+2x+0.75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and 0.75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\times 0.75}}{2}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\times 0.75}}{2}$$

Multiply -4 times 0.75.

$$x=\frac{-2±\sqrt{4-3}}{2}$$

Add 4 to -3.

$$x=\frac{-2±\sqrt{1}}{2}$$

Take the square root of 1.

$$x=\frac{-2±1}{2}$$

Now solve the equation x=\frac{-2±1}{2} when ± is plus. Add -2 to 1.

$$x=-\frac{1}{2}$$

Now solve the equation x=\frac{-2±1}{2} when ± is minus. Subtract 1 from -2.

$$x=-\frac{3}{2}$$

The equation is now solved.

$$x=-\frac{1}{2} x=-\frac{3}{2}$$

Steps for Completing the Square

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

$$-3.75=x^{2}+2x+1-4$$

Subtract 4 from 1 to get -3.

$$-3.75=x^{2}+2x-3$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+2x-3=-3.75$$

Add 3 to both sides.

$$x^{2}+2x=-3.75+3$$

Add -3.75 and 3 to get -0.75.

$$x^{2}+2x=-0.75$$

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+2x+1^{2}=-0.75+1^{2}$$

Square 1.

$$x^{2}+2x+1=-0.75+1$$

Add -0.75 to 1.

$$x^{2}+2x+1=0.25$$

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=0.25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{0.25}$$

Simplify.

$$x+1=\frac{1}{2} x+1=-\frac{1}{2}$$

Subtract 1 from both sides of the equation.

$$x=-\frac{1}{2} x=-\frac{3}{2}$$