Solve x^2+4x+5=5

$$x ^ { 2 } + 4 x + 5 = 5$$

Solve for x

$$x=-4$$

$$x=0$$

Steps Using Factoring

Subtract 5 from both sides.

$$x^{2}+4x+5-5=0$$

Subtract 5 from 5 to get 0.

$$x^{2}+4x=0$$

Factor out x.

$$x\left(x+4\right)=0$$

To find equation solutions, solve x=0 and x+4=0.

$$x=0 x=-4$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}+4x+5=5$$

Subtract 5 from both sides of the equation.

$$x^{2}+4x+5-5=5-5$$

Subtracting 5 from itself leaves 0.

$$x^{2}+4x+5-5=0$$

Subtract 5 from 5.

$$x^{2}+4x=0$$

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

$$x=\frac{-4±\sqrt{4^{2}}}{2}$$

Take the square root of 4^{2}.

$$x=\frac{-4±4}{2}$$

Now solve the equation x=\frac{-4±4}{2} when ± is plus. Add -4 to 4.

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

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-4±4}{2} when ± is minus. Subtract 4 from -4.

$$x=-\frac{8}{2}$$

Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=0 x=-4$$

Steps for Completing the Square

Subtract 5 from both sides.

$$x^{2}+4x+5-5=0$$

Subtract 5 from 5 to get 0.

$$x^{2}+4x=0$$

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

$$x^{2}+4x+2^{2}=2^{2}$$

Square 2.

$$x^{2}+4x+4=4$$

Factor x^{2}+4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2\right)^{2}=4$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{4}$$

Simplify.

$$x+2=2 x+2=-2$$

Subtract 2 from both sides of the equation.

$$x=0 x=-4$$