Chapter 9.5, Problem 4E

To determine

To write the equation in standard form, identify a, b and c then solve using Quadratic formula.

Answer to Problem 4E

Standard form $x^2-4x+12=0$ .

  $a=1,b=-4,c=12$

There exist no real solutions of the equation.

Explanation of Solution

Given:

Equation:

  $x^2-4x=-12$

Calculation:

Converting the given equation in standard form i.e. $a{x}^2+bx+c=0$

  $x^2-4x+12=0$

On comparing the equation with $a{x}^2+bx+c$

  $a=1,b=-4,c=12$

Finding the value of $x$

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substituting the values,

  $x=\frac{-(-4)\pm \sqrt{{(-4)}^2-4(1)(12)}}{2(1)}$

Opening brackets,

  $x=\frac{4\pm \sqrt{16-48}}{2}$

So,

  $x=\frac{4\pm \sqrt{-32}}{2}$

Since, the value of discriminant is negative there exist no real solutions of the equation.