Algebra Examples

$x = \frac{- b + - \sqrt{b^{2} - 4 a c}}{2 a}$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$x = \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}$

Step 2

Rewrite the equation as $\frac{- b - \sqrt{b^{2} - 4 a c}}{2 a} = x$ .

$\frac{- b - \sqrt{b^{2} - 4 a c}}{2 a} = x$

Step 3

Simplify both sides of the equation.

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Step 3.1

Factor $- 1$ out of $- b$ .

$\frac{- (b) - \sqrt{b^{2} - 4 a c}}{2 a} = x$

Step 3.2

Factor $- 1$ out of $- \sqrt{b^{2} - 4 a c}$ .

$\frac{- (b) - (\sqrt{b^{2} - 4 a c})}{2 a} = x$

Step 3.3

Factor $- 1$ out of $- (b) - (\sqrt{b^{2} - 4 a c})$ .

$\frac{- (b + \sqrt{b^{2} - 4 a c})}{2 a} = x$

Step 3.4

Rewrite $- (b + \sqrt{b^{2} - 4 a c})$ as $- 1 (b + \sqrt{b^{2} - 4 a c})$ .

$\frac{- 1 (b + \sqrt{b^{2} - 4 a c})}{2 a} = x$

Step 3.5

Move the negative in front of the fraction.

$- \frac{b + \sqrt{b^{2} - 4 a c}}{2 a} = x$

Step 4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{b^{2} - 4 a c}$ as ${(b^{2} - 4 a c)}^{\frac{1}{2}}$ .

$- \frac{b + {(b^{2} - 4 a c)}^{\frac{1}{2}}}{2 a} = x$