## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

${{x}^{2}}-4x+53=0$
$2-7i\ \text{and }2+7i$ It can be expressed as: $x=\text{ }2+7i$ and $x=\text{ }2+7i$ \begin{align} & x-\left( \text{ }2+7i \right)=0 \\ & \left( x-2 \right)-7i=0 \end{align} Or, \begin{align} & x-\left( 2-7i \right)=0 \\ & \left( x-2 \right)+7i=0 \\ \end{align} Apply the zero-product property $\left( \left( x-2 \right)-7i \right)\left( \left( x-2 \right)+7i \right)=0$ \begin{align} & \left( \left( x-2 \right)-7i \right)\left( \left( x-2 \right)+7i \right)=0 \\ & \left( x-2 \right)\left( x-2 \right)+7i\left( x-2 \right)-7i\left( x-2 \right)-49{{i}^{2}}= \end{align} Combine like terms, Here ${{i}^{2}}=1$ which is a complex entry. ${{\left( x-2 \right)}^{2}}-49\left( {{i}^{2}} \right)=0$ Apply the formula, ${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$ \begin{align} & {{x}^{2}}+4-4x-49\left( -1 \right)=0 \\ & {{x}^{2}}+4-4x+49=0 \\ & {{x}^{2}}-4x+53=0 \end{align}