Chapter ISG, Problem 8.6.1.4P

To determine

To find if the given values for x is correct.

Answer to Problem 8.6.1.4P

I was incorrect.

Explanation of Solution

Given information: Equations given:

  $x^2-2x=63$

Formula used:

Using formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Standard form of a quadratic equation

  $y=a{x}^2+bx+c$

On comparing with the equation,

  $x^2-2x-63=0$

Values of a, b and c

  $\begin{array}{l}a=1\\ b=-2\\ c=-63\\ \end{array}$

Substituting the values in the formula,

  $x=\frac{-(-2)\pm \sqrt{{(-2)}^2-4(1)(-63)}}{2(1)}$

On solving,

  $x=\frac{2\pm \sqrt{4-(-252)}}{2}$

Opening brackets,

  $x=\frac{2\pm \sqrt{4+252}}{2}$

Again,

  $x=\frac{2\pm \sqrt{256}}{2}$

So,

  $x=\frac{2\pm 16}{2}$

Therefore,

  $x=\frac{2+16}{2}$

So,

  $x=\frac{18}{2}$

Or

  $x=9$

Also,

  $x=\frac{2-16}{2}$

So,

  $x=\frac{-14}{2}$

Or

  $x=-7$

So, I was incorrect.