Chapter SH, Problem 9.24EP

To determine

To solve equation by using Quadratic Formula.

Answer to Problem 9.24EP

  $x=15.2,0.8$

Explanation of Solution

Given information :

The function provided is $\frac{1}{2}{x}^2-8x+6=0$

Formula used :

To solve the equation using quadratic formula we need substitute values in the quadratic form given below. This can be found by using $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Here ‘ a’ , ‘ b’ and ‘ c’ are the co-efficient of the given equation.

Here, $a=\frac{1}{2},b=-8\text{ and}c=6$

Calculation :

The given quadratic equation.

  $\frac{1}{2}{x}^2-8x+6=0$

Putting the values in the formula.

  $x=\frac{-(-8)\pm \sqrt{{(-8)}^2-4\times 0.5\times (6)}}{2\times 0.5}$

Simplifying the expression.

  $x=\frac{8\pm \sqrt{64-12}}{1}$

Further simplification

  $x=8\pm \sqrt{52}$

Removing the square root

  $x=8\pm 7.21$

First square root is

  $x=15.21$

Second square root is

  $x=0.79$

Therefore, $x=15.21,0.79$ .