Chapter 9.6, Problem 3AGP

To determine

Find the solution.

Answer to Problem 3AGP

$x=0.5$ or $x=8$

Explanation of Solution

Given Information: $2x^2-17x+8=0$

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

Calculation:

  $2x^2-17x+8=0$

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

  $x^2-\frac{17}{2}x+\frac{8}{2}=0$

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

  $x^2-\frac{17}{2}x+4+{\left(\frac{17}{4}\right)}^2-{\left(\frac{17}{4}\right)}^2=0$

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

  ${\left(x-\frac{17}{4}\right)}^2+4-{\left(\frac{17}{4}\right)}^2=0$

So,

  ${\left(x-\frac{17}{4}\right)}^2+4-\frac{289}{16}=0$

Now,

  ${\left(x-\frac{17}{4}\right)}^2+\frac{64-289}{16}=0$

Now,

  ${\left(x-\frac{17}{4}\right)}^2-\frac{225}{16}=0$

Now, square root of 225 is 15 and square root of 16 is 4.

  ${\left(x-\frac{17}{4}\right)}^2-{\left(\frac{15}{4}\right)}^2=0$

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

  $\left(x-\frac{17}{4}+\frac{15}{4}\right)\left(x-\frac{17}{4}-\frac{15}{4}\right)=0$

Now,

$x=\frac{17}{4}-\frac{15}{4}$ or $x=\frac{17}{4}+\frac{15}{4}$

Now,

$x=\frac{17-15}{4}$ or $x=\frac{17+15}{4}$

Now,

$x=\frac{2}{4}$ or $x=\frac{32}{4}$

Hence,

$x=0.5$ or $x=8$