Chapter 9.6, Problem 25PPS

To determine

The solutions of the equation $10x^2=-7x+6$ using quadratic formula

Answer to Problem 25PPS

  $x=\frac{1}{2},\text{and }x=\frac{-6}{5}$

Explanation of Solution

Given:

The equation,

  $10x^2=-7x+6$

Concept Used:

Quadratic formula: The roots of a quadratic equation $a{x}^2+bx+c=0;\text{ where }a\ne 0$ are:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

In order to solve the given equation $10x^2+7x-6=0$ , since it is in the descending order of exponents, so comparing with the general equation $a{x}^2+bx+c=0$ , the value of the coefficient a, b, and c is given by

  $a=10,b=7,\text{ and }c=-6$

Now, above quadratic equation $10y^2+7y-6=0$ can be solved using quadratic formula as shown below,

  $\begin{array}{c}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-\left(7\right)\pm \sqrt{{\left(7\right)}^2-4\left(10\right)\left(-6\right)}}{2\left(10\right)}\\ =\frac{-7\pm \sqrt{289}}{20}\\ =\frac{-7\pm 17}{20}\\ =\frac{-7\pm 17}{20}\\ x=\frac{-7+17}{20},\text{and }x=\frac{-7-17}{20}\\ x=\frac{10}{20},\text{and }x=\frac{-24}{20}\\ x=\frac{1}{2},\text{and }x=\frac{-6}{5}\end{array}$

Thus, the solutions of the given question are, $x=\frac{1}{2},\text{and }x=\frac{-6}{5}$ .