Chapter 9.6, Problem 59PFA

(a)

To determine

Solve the error.

Answer to Problem 59PFA

Option D and Option F

Explanation of Solution

Given Information: $8x^2-3x=9$

Formula Used: $D=b^2-4ac$

Calculation:

  $8x^2-3x=9$

So, simplify

  $8x^2-3x-9=0$

Now, use formula $D=b^2-4ac$ to check if solution of $x$ exist or not.

As $a=8,b=-3$ and $c=-9$

  $D={\left(-3\right)}^2-4\times 8\times \left(-9\right)$

Now,

  $D=9+288$

So,

Option D as c value is -9, not 9.

Option F as ${\left(-3\right)}^2=9$ , not -9

(b)

To determine

Solve the solution.

Answer to Problem 59PFA

Option B and Option E

Explanation of Solution

Given Information: $8x^2-3x=9$

Formula Used: $D=b^2-4ac$ and $x=\frac{-b\pm \sqrt{D}}{2a}$

Calculation:

  $8x^2-3x=9$

So, simplify

  $8x^2-3x-9=0$

Now, use formula $D=b^2-4ac$ to check if solution of $x$ exist or not.

As $a=8,b=-3$ and $c=-9$

  $D={\left(-3\right)}^2-4\times 8\times \left(-9\right)$

Now,

  $D=9+288$

So,

  $D=297$

As, $D$ equal to positive so $x$ has 2 real solution.

  $x=\frac{-b\pm \sqrt{D}}{2a}$

So,

  $x=\frac{-\left(-3\right)\pm \sqrt{297}}{2\times 8}$

Now, square root of 297 is 17.23.

  $x=\frac{3\pm 17.23}{16}$

Now,

  $x=\frac{3+17.23}{16}$ or $x=\frac{3-17.23}{16}$

Now,

  $x=\frac{20.23}{16}$ or $x=\frac{-14.23}{16}$

Hence,

  $x=1.3$ or $x=-0.9$

So,

Option B as $x=1.3$

Option E as $x=-0.9$

(c)

To determine

Solve the strategy to reduce error.

Answer to Problem 59PFA

Make the equation in the general form $a{x}^2+bx+c=0$

Explanation of Solution

Given Information: $8x^2-3x=9$

Formula Used: $D=b^2-4ac$ and $x=\frac{-b\pm \sqrt{D}}{2a}$

Calculation:

First make the equation in the general form $a{x}^2+bx+c=0$

  $8x^2-3x=9$

So, simplify

  $8x^2-3x-9=0$

Now, use formula $D=b^2-4ac$ to check if solution of $x$ exist or not.

As $a=8,b=-3$ and $c=-9$

  $D={\left(-3\right)}^2-4\times 8\times \left(-9\right)$

Now,

  $D=9+288$

So,

  $D=297$

As, $D$ equal to positive so $x$ has 2 real solution.

  $x=\frac{-b\pm \sqrt{D}}{2a}$

So,

  $x=\frac{-\left(-3\right)\pm \sqrt{297}}{2\times 8}$

Now, square root of 297 is 17.23.

  $x=\frac{3\pm 17.23}{16}$

Now,

  $x=\frac{3+17.23}{16}$ or $x=\frac{3-17.23}{16}$

Now,

  $x=\frac{20.23}{16}$ or $x=\frac{-14.23}{16}$

Hence,

  $x=1.3$ or $x=-0.9$