Question

consider the following radical equation: w = √(w + 42). the radical expression is already isolated, so clear the radical and rewrite as a polynomial equation. do not yet balance the equation or solve for w. balance the equation and rewrite in factored form: = 0. solve for w as an integer or simplified fraction: w = . question help: video

Explanation:

Step1: Clear the radical

Square both sides of the equation $w = \sqrt{w + 42}$ to get $w^{2}=w + 42$.

Step2: Balance the equation and factor

Rearrange $w^{2}=w + 42$ to $w^{2}-w - 42=0$. Factor the quadratic equation: $w^{2}-w - 42=(w - 7)(w+ 6)=0$.

Step3: Solve for $w$

Set each factor equal to zero: $w - 7=0$ gives $w = 7$; $w + 6=0$ gives $w=-6$. But when we substitute $w=-6$ into the original equation, the right - hand side $\sqrt{-6 + 42}=\sqrt{36}=6
eq - 6$. So we discard $w=-6$.

Answer:

$w = 7$