Solve (x ^ 2)/4 - 4x + 16 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{x^{2}}{4}-4x+16$$

Evaluate

$\frac{\left(x-8\right)^{2}}{4}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $-4x+16$ times $\frac{4}{4}$.

$$\frac{x^{2}}{4}+\frac{4\left(-4x+16\right)}{4}$$

Since $\frac{x^{2}}{4}$ and $\frac{4\left(-4x+16\right)}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+4\left(-4x+16\right)}{4}$$

Do the multiplications in $x^{2}+4\left(-4x+16\right)$.

$$\frac{x^{2}-16x+64}{4}$$

Factor

$\frac{\left(x-8\right)^{2}}{4}$

Solution Steps

Factor out $\frac{1}{4}$.

$$\frac{x^{2}-16x+64}{4}$$

Consider $x^{2}-16x+64$. Use the perfect square formula, $a^{2}-2ab+b^{2}=\left(a-b\right)^{2}$, where $a=x$ and $b=8$.

$$\left(x-8\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(x-8\right)^{2}}{4}$$