Solve Using the Quadratic Formula 1/2x^2+1/14x-1=0

$\frac{1}{2} x^{2} + \frac{1}{14} x - 1 = 0$

Simplify each term.

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Combine $\frac{1}{2}$ and $x^{2}$ .

$\frac{x^{2}}{2} + \frac{1}{14} x - 1 = 0$

Combine $\frac{1}{14}$ and $x$ .

$\frac{x^{2}}{2} + \frac{x}{14} - 1 = 0$

Multiply through by the least common denominator $14$ , then simplify.

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Apply the distributive property.

$14 (\frac{x^{2}}{2}) + 14 (\frac{x}{14}) + 14 \cdot - 1 = 0$

Simplify.

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Cancel the common factor of $2$ .

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Factor $2$ out of $14$ .

$2 (7) (\frac{x^{2}}{2}) + 14 (\frac{x}{14}) + 14 \cdot - 1 = 0$

Cancel the common factor.

$2 \cdot (7 (\frac{x^{2}}{2})) + 14 (\frac{x}{14}) + 14 \cdot - 1 = 0$

Rewrite the expression.

$7 x^{2} + 14 (\frac{x}{14}) + 14 \cdot - 1 = 0$

Cancel the common factor of $14$ .

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Cancel the common factor.

$7 x^{2} + 14 (\frac{x}{14}) + 14 \cdot - 1 = 0$

Rewrite the expression.

$7 x^{2} + x + 14 \cdot - 1 = 0$

Multiply $14$ by $- 1$ .

$7 x^{2} + x - 14 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 7$ , $b = 1$ , and $c = - 14$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (7 \cdot - 14)}}{2 \cdot 7}$

Simplify.

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Simplify the numerator.

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One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 7 \cdot - 14}}{2 \cdot 7}$

Multiply $- 4$ by $7$ .

$x = \frac{- 1 \pm \sqrt{1 - 28 \cdot - 14}}{2 \cdot 7}$

Multiply $- 28$ by $- 14$ .

$x = \frac{- 1 \pm \sqrt{1 + 392}}{2 \cdot 7}$

Add $1$ and $392$ .

$x = \frac{- 1 \pm \sqrt{393}}{2 \cdot 7}$

Multiply $2$ by $7$ .

$x = \frac{- 1 \pm \sqrt{393}}{14}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1 \pm \sqrt{393}}{14}$

Decimal Form:

$x = 1.34458768 \dots, - 1.48744482 \dots$

Solve Using the Quadratic Formula 1/2x^2+1/14x-1=0

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