Chapter 9.5, Problem 51PFA

To determine

Find the solution.

Answer to Problem 51PFA

  $x=4$ or $x=6$

Explanation of Solution

Given Information: $-3x^2+30x-72=0$

Formula Used: $a^2-2ab+b^2={(a-b)}^2$ and $a^2-b^2=(a+b)(a-b)$

Calculation:

  $-3x^2+30x-72=0$

So,

  $3x^2-30x+72=0$

Now, to make coefficient of $x^2=1$ , divide the equation by 3.

  $x^2-10x+24=0$

Now, adding & subtracting the square of half the coefficient of x.

  $x^2-10x+24+{\left(\frac{10}{2}\right)}^2-{\left(\frac{10}{2}\right)}^2=0$

Now use formula, $a^2-2ab+b^2={(a-b)}^2$

  ${\left(x-5\right)}^2+24-5^2=0$

So,

  ${\left(x-5\right)}^2+24-25=0$

So,

  ${\left(x-5\right)}^2-1=0$

Now, square root of 1 is 1

  ${\left(x-5\right)}^2-1^2=0$

Now use formula, $a^2-b^2=(a+b)(a-b)$

  $\left(x-5+1\right)\left(x-5-1\right)=0$

So,

  $x=5-1$ or $x=5+1$

Hence,

  $x=4$ or $x=6$