Solve {l}{1000144-(x+5)^2}{(x-7)(x-17)}

$$\left. \begin{array} { l } { 1000144 - ( x + 5 ) ^ { 2 } } \\ { ( x - 7 ) ( x - 17 ) } \end{array} \right.$$

Least Common Multiple

$$\left(x-17\right)\left(x-7\right)\left(\left(x+5\right)^{2}-1000144\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$1000144-\left(x+5\right)^{2}=-\left(x-\left(-4\sqrt{62509}-5\right)\right)\left(x-\left(4\sqrt{62509}-5\right)\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(x-17\right)\left(x-7\right)\left(x-\left(-4\sqrt{62509}-5\right)\right)\left(x-\left(4\sqrt{62509}-5\right)\right)$$

Expand the expression.

$$x^{4}-14x^{3}-1000240x^{2}[phone]x-119014161$$

Evaluate

$$-\left(x+5\right)^{2}+1000144,\ \left(x-17\right)\left(x-7\right)$$