Solve for x x^2-3/4x-7/64=0

$x^{2} - \frac{3}{4} x - \frac{7}{64} = 0$

Step 1

Simplify each term.

Combine $x$ and $\frac{3}{4}$ .

$x^{2} - \frac{x \cdot 3}{4} - \frac{7}{64} = 0$

Move $3$ to the left of $x$ .

$x^{2} - \frac{3 x}{4} - \frac{7}{64} = 0$

Step 2

Multiply through by the least common denominator $64$ , then simplify.

Apply the distributive property.

$64 x^{2} + 64 (- \frac{3 x}{4}) + 64 (- \frac{7}{64}) = 0$

Simplify.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$64 x^{2} + 64 (\frac{- 3 x}{4}) + 64 (- \frac{7}{64}) = 0$

Factor $4$ out of $64$ .

$64 x^{2} + 4 (16) (\frac{- 3 x}{4}) + 64 (- \frac{7}{64}) = 0$

Cancel the common factor.

$64 x^{2} + 4 \cdot (16 (\frac{- 3 x}{4})) + 64 (- \frac{7}{64}) = 0$

Rewrite the expression.

$64 x^{2} + 16 (- 3 x) + 64 (- \frac{7}{64}) = 0$

Multiply $- 3$ by $16$ .

$64 x^{2} - 48 x + 64 (- \frac{7}{64}) = 0$

Cancel the common factor of $64$ .

Move the leading negative in $- \frac{7}{64}$ into the numerator.

$64 x^{2} - 48 x + 64 (\frac{- 7}{64}) = 0$

Cancel the common factor.

$64 x^{2} - 48 x + 64 (\frac{- 7}{64}) = 0$

Rewrite the expression.

$64 x^{2} - 48 x - 7 = 0$

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 $a = 64$ , $b = - 48$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

$\frac{48 \pm \sqrt{{(- 48)}^{2} - 4 \cdot (64 \cdot - 7)}}{2 \cdot 64}$

Step 5

Simplify.

Simplify the numerator.

Raise $- 48$ to the power of $2$ .

$x = \frac{48 \pm \sqrt{2304 - 4 \cdot 64 \cdot - 7}}{2 \cdot 64}$

Multiply $- 4 \cdot 64 \cdot - 7$ .

Multiply $- 4$ by $64$ .

$x = \frac{48 \pm \sqrt{2304 - 256 \cdot - 7}}{2 \cdot 64}$

Multiply $- 256$ by $- 7$ .

$x = \frac{48 \pm \sqrt{2304 + 1792}}{2 \cdot 64}$

Add $2304$ and $1792$ .

$x = \frac{48 \pm \sqrt{4096}}{2 \cdot 64}$

Rewrite $4096$ as $64^{2}$ .

$x = \frac{48 \pm \sqrt{64^{2}}}{2 \cdot 64}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{48 \pm 64}{2 \cdot 64}$

Multiply $2$ by $64$ .

$x = \frac{48 \pm 64}{128}$

Simplify $\frac{48 \pm 64}{128}$ .

$x = \frac{3 \pm 4}{8}$

Step 6

The final answer is the combination of both solutions.

$x = \frac{7}{8}, - \frac{1}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{8}, - \frac{1}{8}$

Decimal Form:

$x = 0.875, - 0.125$

Solve for x x^2-3/4x-7/64=0

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