Complete the Square x^2+3/4x

$x^{2} + \frac{3}{4} x$

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

$x^{2} + \frac{3 x}{4}$

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1, b = \frac{3}{4}, c = 0$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{\frac{3}{4}}{2 (1)}$

Simplify the right side.

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Multiply the numerator by the reciprocal of the denominator.

$d = \frac{3}{4} \cdot \frac{1}{2 (1)}$

Cancel the common factor of $1$ .

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Cancel the common factor.

$d = \frac{3}{4} \cdot \frac{1}{2 \cdot 1}$

Rewrite the expression.

$d = \frac{3}{4} \cdot \frac{1}{2}$

Multiply $\frac{3}{4} \cdot \frac{1}{2}$ .

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Multiply $\frac{3}{4}$ and $\frac{1}{2}$ .

$d = \frac{3}{4 \cdot 2}$

Multiply $4$ by $2$ .

$d = \frac{3}{8}$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

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Simplify each term.

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Simplify the numerator.

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Apply the product rule to $\frac{3}{4}$ .

$e = 0 - \frac{\frac{3^{2}}{4^{2}}}{4 (1)}$

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

$e = 0 - \frac{\frac{9}{4^{2}}}{4 (1)}$

Raise $4$ to the power of $2$ .

$e = 0 - \frac{\frac{9}{16}}{4 (1)}$

Multiply $4$ by $1$ .

$e = 0 - \frac{\frac{9}{16}}{4}$

Multiply the numerator by the reciprocal of the denominator.

$e = 0 - (\frac{9}{16} \cdot \frac{1}{4})$

Multiply $\frac{9}{16} \cdot \frac{1}{4}$ .

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Multiply $\frac{9}{16}$ and $\frac{1}{4}$ .

$e = 0 - \frac{9}{16 \cdot 4}$

Multiply $16$ by $4$ .

$e = 0 - \frac{9}{64}$

Subtract $\frac{9}{64}$ from $0$ .

$e = - \frac{9}{64}$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $a {(x + d)}^{2} + e$ .

${(x + \frac{3}{8})}^{2} - \frac{9}{64}$

Complete the Square x^2+3/4x

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