Chapter 8, Problem 27PT

To determine

To Evaluate: Evaluate the given equation and check the answer.

Answer to Problem 27PT

The solutions are $x=-4$ and 6.

Thus the obtained value for $x$ are correct as they satisfied the given equation..

Explanation of Solution

Given information:

  

Calculation:

The given equation as follows:

  $x^2-6x+4x-24=0$

  $x(x-6)+4(x-6)=0$

  $(x+4)(x-6)=0$

  $\Rightarrow x+4=0$

  $x-6=0$

  $\Rightarrow x=-4$

  $x=6$

Hence, the solutions are $x=-4$ and 6

Check:

Substitute $x=-4$in the left hand side part of the given equation.

  $={(-4)}^2-2(-4)-24$

  $=16+8-24$

  $=0$

Similarly, Substitute $x=6$ in the left hand side part of the given equation.

  $={(6)}^2-2(6)-24$

  $=36-12-24$

  $=0$

Thus the obtained value for $x$ are correct as they satisfied the given equation.