Chapter 46, Problem 71A

To determine

To solve for the unknown value in the given equation.

Answer to Problem 71A

  $P=\pm 2.053$.

Explanation of Solution

Given information:

The given equation is $\frac{P^2-186.73}{5.65P}=\frac{-23.30P}{3.04}$.

Calculation:

We have been given the equation as $\frac{P^2-186.73}{5.65P}=\frac{-23.30P}{3.04}$.

We will perform some basic mathematical operation to solve the given equation as below.

  $\frac{P^2-186.73}{5.65P}=\frac{-23.30P}{3.04}$

  $\Rightarrow 3.04(P^2-186.73)=-23.30P\times 5.65P\left\{\text{Cross multiply}\right\}$

  $\Rightarrow 3.04P^2-567.6592=-131.645P^2$

  $\Rightarrow 3.04P^2+131.645P^2=567.6592\text{ {Bringing the variable on one side}}$

  $\Rightarrow 134.685P^2=567.6592\left\{\text{Simplify}\right\}$

  $\Rightarrow \frac{134.685}{134.685}{P}^2=\frac{567.6592}{134.685}\left\{\text{Dividing}\text{by}134.685\text{on}\text{both}\text{sides}\right\}$

  $\Rightarrow P^2=4.215$

  $\Rightarrow P=\pm \sqrt{4.215}$

  $\Rightarrow P=\pm 2.053$

  $\text{Check:}$

  $\frac{P^2-186.73}{5.65P}=\frac{-23.30P}{3.04}$

  $\frac{{(2.053)}^2-186.73}{5.65\times 2.053}=\frac{-23.30\times 2.053}{3.04}$

  $\frac{4.215-186.73}{11.599}=\frac{-47.835}{3.04}$

  $\frac{-182.515}{11.599}=\frac{-47.835}{3.04}$

  $-15.735\approx 15.735$

Hence, solution of the equation will be given by-

  $P=\pm 2.053$.