Solve Using the Quadratic Formula 1/3x^2+1/15x-1=0

$\frac{1}{3} x^{2} + \frac{1}{15} x - 1 = 0$

Step 1

Simplify the left side.

Simplify each term.

Combine $\frac{1}{3}$ and $x^{2}$ .

$\frac{x^{2}}{3} + \frac{1}{15} x - 1 = 0$

Combine $\frac{1}{15}$ and $x$ .

$\frac{x^{2}}{3} + \frac{x}{15} - 1 = 0$

Step 2

Multiply through by the least common denominator $15$ , then simplify.

Apply the distributive property.

$15 (\frac{x^{2}}{3}) + 15 (\frac{x}{15}) + 15 \cdot - 1 = 0$

Simplify.

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$3 (5) (\frac{x^{2}}{3}) + 15 (\frac{x}{15}) + 15 \cdot - 1 = 0$

Cancel the common factor.

$3 \cdot (5 (\frac{x^{2}}{3})) + 15 (\frac{x}{15}) + 15 \cdot - 1 = 0$

Rewrite the expression.

$5 x^{2} + 15 (\frac{x}{15}) + 15 \cdot - 1 = 0$

Cancel the common factor of $15$ .

Cancel the common factor.

$5 x^{2} + 15 (\frac{x}{15}) + 15 \cdot - 1 = 0$

Rewrite the expression.

$5 x^{2} + x + 15 \cdot - 1 = 0$

Multiply $15$ by $- 1$ .

$5 x^{2} + x - 15 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 5$ , $b = 1$ , and $c = - 15$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (5 \cdot - 15)}}{2 \cdot 5}$

Step 5

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 5 \cdot - 15}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 15$ .

Multiply $- 4$ by $5$ .

$x = \frac{- 1 \pm \sqrt{1 - 20 \cdot - 15}}{2 \cdot 5}$

Multiply $- 20$ by $- 15$ .

$x = \frac{- 1 \pm \sqrt{1 + 300}}{2 \cdot 5}$

Add $1$ and $300$ .

$x = \frac{- 1 \pm \sqrt{301}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 1 \pm \sqrt{301}}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1 \pm \sqrt{301}}{10}$

Decimal Form:

$x = 1.63493515 \dots, - 1.83493515 \dots$

Solve Using the Quadratic Formula 1/3x^2+1/15x-1=0

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