Chapter 12, Problem 9CT

To determine

To calculate: The values of $x$ from the equation $7x^2-3x=0$ solve by using the most appropriate method.

Answer to Problem 9CT

The values are $x=0\text{or}x=\frac{3}{7}$

Explanation of Solution

Given information:

The equation is given as:

  $7x^2-3x=0$

Formula used:

Methods for solving a Quadratic equation,

If the equation is in this form $a{x}^2+bx+c=0$ then use quadratic method.

If the equation is in this form $a{x}^2+bx=0$ then use Factoring method.

If the equation is in this form $a{x}^2+c=0$ then use property of square roots of equal numbers.

If the equation is in this form $x^2+bx+c=0$ and $\text{b}$ is an even number then use Completing the square method.

Calculation:

Since, the provided equation $7x^2-3x=0$ is in the form $a{x}^2+bx=0$ so, using the Factoring method as,

  $7x^2-3x=0$

In equation $x$ is common so take common $x$ as,

  $x\left(7x-3\right)=0$

Furthermore,

  $x=0\text{or}7x-3=0$

Therefore,

  $x=0\text{or}x=\frac{3}{7}$

The best method for solving $2y^2+8y=0$ is factoring.

So, the values are $x=0\text{or}x=\frac{3}{7}$ .