Solve x^2+5x-5=0quadb

$$x ^ { 2 } + 5 x - 5 = 0 \quad b$$

Solve for x

$$x = \frac{3 \sqrt{5} - 5}{2} = 0.8541019662496847$$

$$x = \frac{-3 \sqrt{5} - 5}{2} = -5.854101966249685$$

Steps Using the Quadratic Formula

Anything times zero gives zero.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 5 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-5\right)}}{2}$$

Square 5.

$$x=\frac{-5±\sqrt{25-4\left(-5\right)}}{2}$$

Multiply -4 times -5.

$$x=\frac{-5±\sqrt{25+20}}{2}$$

Add 25 to 20.

$$x=\frac{-5±\sqrt{45}}{2}$$

Take the square root of 45.

$$x=\frac{-5±3\sqrt{5}}{2}$$

Now solve the equation x=\frac{-5±3\sqrt{5}}{2} when ± is plus. Add -5 to 3\sqrt{5}.

$$x=\frac{3\sqrt{5}-5}{2}$$

Now solve the equation x=\frac{-5±3\sqrt{5}}{2} when ± is minus. Subtract 3\sqrt{5} from -5.

$$x=\frac{-3\sqrt{5}-5}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{5}-5}{2} x=\frac{-3\sqrt{5}-5}{2}$$

Steps for Completing the Square

Anything times zero gives zero.

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

Add 5 to both sides. Anything plus zero gives itself.

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

Divide 5, the coefficient of the x term, by 2 to get \frac{5}{2}. Then add the square of \frac{5}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=5+\left(\frac{5}{2}\right)^{2}$$

Square \frac{5}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+5x+\frac{25}{4}=5+\frac{25}{4}$$

Add 5 to \frac{25}{4}.

$$x^{2}+5x+\frac{25}{4}=\frac{45}{4}$$

Factor x^{2}+5x+\frac{25}{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}.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{45}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{45}{4}}$$

Simplify.

$$x+\frac{5}{2}=\frac{3\sqrt{5}}{2} x+\frac{5}{2}=-\frac{3\sqrt{5}}{2}$$

Subtract \frac{5}{2} from both sides of the equation.

$$x=\frac{3\sqrt{5}-5}{2} x=\frac{-3\sqrt{5}-5}{2}$$

Solve for b (complex solution)

$$b\in \mathrm{C}$$

$$x=\frac{3\sqrt{5}-5}{2}\text{ or }x=\frac{-3\sqrt{5}-5}{2}$$

Solve for b

$$b\in \mathrm{R}$$

$$x=\frac{3\sqrt{5}-5}{2}\text{ or }x=\frac{-3\sqrt{5}-5}{2}$$