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

w = -8, 1

Explanation

Given the equation:

`√(-7w+8)=w`

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

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