Question

Solve for w, where w is a real number.√-7w+8=w(If there is more than one solution, separate them with commas.)

Answer 1

Answer

w = -8, 1

Step-by-step explanation

Given the equation:

$\sqrt{-7w+8}=w$

Squaring both sides of the equation and reordering the resulting terms:

$\begin{gathered} (\sqrt{-7w+8})^2=w^2 \\ -7w+8=w^2 \\ 0=w^2+7w-8 \end{gathered}$

This is a quadratic function with coefficients a = 1, b = 7, and c = -8. Applying the quadratic formula, we get the next solutions:

$\begin{gathered} w_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ w_{1,2}=\frac{-7\pm\sqrt{7^2-4\cdot1\cdot(-8)}}{2\cdot1} \\ w_{1,2}=\frac{-7\pm\sqrt{81}}{2} \\ w_1=\frac{-7+9}{2}=1 \\ w_2=\frac{-7-9}{2}=-8 \end{gathered}$