Algebra Examples

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

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = - 2$ , and $c = c$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (1 \cdot c)}}{2 \cdot 1}$

Simplify.

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Simplify the numerator.

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Raise $- 2$ to the power of $2$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 1 \cdot c}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot c}}{2 \cdot 1}$

Factor $4$ out of $4 - 4 c$ .

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Factor $4$ out of $4$ .

$x = \frac{2 \pm \sqrt{4 (1) - 4 c}}{2 \cdot 1}$

Factor $4$ out of $- 4 c$ .

$x = \frac{2 \pm \sqrt{4 (1) + 4 (- c)}}{2 \cdot 1}$

Factor $4$ out of $4 (1) + 4 (- c)$ .

$x = \frac{2 \pm \sqrt{4 (1 - c)}}{2 \cdot 1}$

Rewrite $4 (1 - c)$ as $2^{2} (1^{2} - c)$ .

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Rewrite $4$ as $2^{2}$ .

$x = \frac{2 \pm \sqrt{2^{2} (1 - c)}}{2 \cdot 1}$

Rewrite $1$ as $1^{2}$ .

$x = \frac{2 \pm \sqrt{2^{2} (1^{2} - c)}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{2 \pm 2 \sqrt{1^{2} - c}}{2 \cdot 1}$

One to any power is one.

$x = \frac{2 \pm 2 \sqrt{1 - c}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{2 \pm 2 \sqrt{1 - c}}{2}$

Simplify $\frac{2 \pm 2 \sqrt{1 - c}}{2}$ .

$x = 1 \pm \sqrt{1 - c}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Simplify the numerator.

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Raise $- 2$ to the power of $2$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 1 \cdot c}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot c}}{2 \cdot 1}$

Factor $4$ out of $4 - 4 c$ .

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Factor $4$ out of $4$ .

$x = \frac{2 \pm \sqrt{4 (1) - 4 c}}{2 \cdot 1}$

Factor $4$ out of $- 4 c$ .

$x = \frac{2 \pm \sqrt{4 (1) + 4 (- c)}}{2 \cdot 1}$

Factor $4$ out of $4 (1) + 4 (- c)$ .

$x = \frac{2 \pm \sqrt{4 (1 - c)}}{2 \cdot 1}$

Rewrite $4 (1 - c)$ as $2^{2} (1^{2} - c)$ .

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Rewrite $4$ as $2^{2}$ .

$x = \frac{2 \pm \sqrt{2^{2} (1 - c)}}{2 \cdot 1}$

Rewrite $1$ as $1^{2}$ .

$x = \frac{2 \pm \sqrt{2^{2} (1^{2} - c)}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{2 \pm 2 \sqrt{1^{2} - c}}{2 \cdot 1}$

One to any power is one.

$x = \frac{2 \pm 2 \sqrt{1 - c}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{2 \pm 2 \sqrt{1 - c}}{2}$

Simplify $\frac{2 \pm 2 \sqrt{1 - c}}{2}$ .

$x = 1 \pm \sqrt{1 - c}$

Change the $\pm$ to $+$ .

$x = 1 + \sqrt{1 - c}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Simplify the numerator.

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Raise $- 2$ to the power of $2$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 1 \cdot c}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot c}}{2 \cdot 1}$

Factor $4$ out of $4 - 4 c$ .

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Factor $4$ out of $4$ .

$x = \frac{2 \pm \sqrt{4 (1) - 4 c}}{2 \cdot 1}$

Factor $4$ out of $- 4 c$ .

$x = \frac{2 \pm \sqrt{4 (1) + 4 (- c)}}{2 \cdot 1}$

Factor $4$ out of $4 (1) + 4 (- c)$ .

$x = \frac{2 \pm \sqrt{4 (1 - c)}}{2 \cdot 1}$

Rewrite $4 (1 - c)$ as $2^{2} (1^{2} - c)$ .

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Rewrite $4$ as $2^{2}$ .

$x = \frac{2 \pm \sqrt{2^{2} (1 - c)}}{2 \cdot 1}$

Rewrite $1$ as $1^{2}$ .

$x = \frac{2 \pm \sqrt{2^{2} (1^{2} - c)}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{2 \pm 2 \sqrt{1^{2} - c}}{2 \cdot 1}$

One to any power is one.

$x = \frac{2 \pm 2 \sqrt{1 - c}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{2 \pm 2 \sqrt{1 - c}}{2}$

Simplify $\frac{2 \pm 2 \sqrt{1 - c}}{2}$ .

$x = 1 \pm \sqrt{1 - c}$

Change the $\pm$ to $-$ .

$x = 1 - \sqrt{1 - c}$

The final answer is the combination of both solutions.

$x = 1 + \sqrt{1 - c}$

$x = 1 - \sqrt{1 - c}$