Solve Using the Quadratic Formula 1/2x^2-1/4=3/16x

$\frac{1}{2} x^{2} - \frac{1}{4} = \frac{3}{16} x$

Move all terms to the left side of the equation and simplify.

Simplify the left side.

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

$\frac{x^{2}}{2} - \frac{1}{4} = \frac{3}{16} x$

Simplify the right side.

Combine $\frac{3}{16}$ and $x$ .

$\frac{x^{2}}{2} - \frac{1}{4} = \frac{3 x}{16}$

Subtract $\frac{3 x}{16}$ from both sides of the equation.

$\frac{x^{2}}{2} - \frac{1}{4} - \frac{3 x}{16} = 0$

Multiply through by the least common denominator $16$ , then simplify.

Apply the distributive property.

$16 (\frac{x^{2}}{2}) + 16 (- \frac{1}{4}) + 16 (- \frac{3 x}{16}) = 0$

Simplify.

Cancel the common factor of $2$ .

Factor $2$ out of $16$ .

$2 (8) (\frac{x^{2}}{2}) + 16 (- \frac{1}{4}) + 16 (- \frac{3 x}{16}) = 0$

Cancel the common factor.

$2 \cdot (8 (\frac{x^{2}}{2})) + 16 (- \frac{1}{4}) + 16 (- \frac{3 x}{16}) = 0$

Rewrite the expression.

$8 x^{2} + 16 (- \frac{1}{4}) + 16 (- \frac{3 x}{16}) = 0$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$8 x^{2} + 16 (\frac{- 1}{4}) + 16 (- \frac{3 x}{16}) = 0$

Factor $4$ out of $16$ .

$8 x^{2} + 4 (4) (\frac{- 1}{4}) + 16 (- \frac{3 x}{16}) = 0$

Cancel the common factor.

$8 x^{2} + 4 \cdot (4 (\frac{- 1}{4})) + 16 (- \frac{3 x}{16}) = 0$

Rewrite the expression.

$8 x^{2} + 4 \cdot - 1 + 16 (- \frac{3 x}{16}) = 0$

Multiply $4$ by $- 1$ .

$8 x^{2} - 4 + 16 (- \frac{3 x}{16}) = 0$

Cancel the common factor of $16$ .

Move the leading negative in $- \frac{3 x}{16}$ into the numerator.

$8 x^{2} - 4 + 16 (\frac{- 3 x}{16}) = 0$

Cancel the common factor.

$8 x^{2} - 4 + 16 (\frac{- 3 x}{16}) = 0$

Rewrite the expression.

$8 x^{2} - 4 - 3 x = 0$

Move $- 4$ .

$8 x^{2} - 3 x - 4 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 8$ , $b = - 3$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (8 \cdot - 4)}}{2 \cdot 8}$

Simplify.

Simplify the numerator.

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 8 \cdot - 4}}{2 \cdot 8}$

Multiply $- 4$ by $8$ .

$x = \frac{3 \pm \sqrt{9 - 32 \cdot - 4}}{2 \cdot 8}$

Multiply $- 32$ by $- 4$ .

$x = \frac{3 \pm \sqrt{9 + 128}}{2 \cdot 8}$

Add $9$ and $128$ .

$x = \frac{3 \pm \sqrt{137}}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{3 \pm \sqrt{137}}{16}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 \pm \sqrt{137}}{16}$

Decimal Form:

$x = 0.91904374 \dots, - 0.54404374 \dots$

Solve Using the Quadratic Formula 1/2x^2-1/4=3/16x

Related Questions

Support LCMGCF.com by disabling your adblocker.