Chapter 9.5, Problem 46PFA

To determine

Solve the equation.

Answer to Problem 46PFA

(c) Option C $x=4+\sqrt{33}$

Option E $x=4-\sqrt{33}$

(d)

Option A

The axis of symmetry is x=4.

Explanation of Solution

Given Information: $3x^2-24x=51$

Formula Used: Factorization and $D=b^2-4ac$ , $a^2-2ab+b^2={(a-b)}^2$

Calculation:

  $3x^2-24x=51$

(a) First step is to make the coefficient of $x^2$ is 1.

So,

  $x^2-8x=17$

(b)

Now have to add the square of half the coefficient of x.

i.e. 16

(c)

  $x^2-8x+16=17+16$

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

So,

  ${\left(x-4\right)}^2=33$

Now,

  ${\left(x-4\right)}^2-33=0$

Now, square root of 33 is $\sqrt{33}$

  ${\left(x-4\right)}^2-{\left(\sqrt{33}\right)}^2=0$

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

  $\left(x-4+\sqrt{33}\right)\left(x-4-\sqrt{33}\right)=0$

Now,

  $x=4-\sqrt{33}$ or $x=4+\sqrt{33}$

Option C $x=4+\sqrt{33}$

Option E $x=4-\sqrt{33}$

(d)

Option A

The axis of symmetry is x=4.