Solve x^2-7x+{left(-7/2right)}^2

$${ x }^{ 2 } -7x+ { \left( \frac{ -7 }{ 2 } \right) }^{ 2 }$$

Evaluate

$$\frac{\left(2x-7\right)^{2}}{4}$$

Solution Steps

Fraction \frac{-7}{2} can be rewritten as -\frac{7}{2} by extracting the negative sign.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}$$

Calculate -\frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$x^{2}-7x+\frac{49}{4}$$

Factor

$$\frac{\left(2x-7\right)^{2}}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{4x^{2}-28x+49}{4}$$

Consider 4x^{2}-28x+49. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=2x and b=7.

$$\left(2x-7\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(2x-7\right)^{2}}{4}$$