Chapter 8.2, Problem 32PPS

To determine

To solve the given equation.

Answer to Problem 32PPS

  $w=1.83$

Explanation of Solution

Given:

  $w\left(4w+6\right)+2w=2\left(2w^2+7w-3\right)$

Calculation:

Solving the given equation,

  $\Rightarrow w\left(4w+6\right)+2w=2\left(2w^2+7w-3\right)$

  $\Rightarrow 4w^2+w+2w=4w^2+14w-6$

[Solving the brackets]

  $\Rightarrow 4w^2+w+2w-4w^2-14w+6=0$

[Solving both sides]

  $\Rightarrow 4w^2-4w^2+w+2w-14w+6=0$

[Rearranging the terms]

  $\Rightarrow -11w+6=0$

  $\Rightarrow 11w=6$

[Adding $11w$ both sides]

  $\begin{array}{l}\Rightarrow w=\frac{11}{6}\\ \Rightarrow w=1.83\end{array}$

Conclusion:

Therefore, the value of $w=1.83$ .