Chapter 9.5, Problem 36P

Writing Discuss the strategies of graphing, factoring, and completing the square for solving the quadratic equation $x^2+4x-6=0.$

To determine

To discuss the strategies of graphing, factoring and completing the square.

Answer to Problem 36P

Hence discussed the strategies of graphing, factoring and completing the square.

Explanation of Solution

Given information: Given equation is $x^2+4x-6=0.$

Calculation:

By graph, we graph the related function $y=x^2+4x-6$ and identify the $x$ -intercepts which are the solutions of the equation.

By factor, we factor the left side then apply zero product property by equating each factor

To solve each equation yields the solution to the equation.

By complete the square, isolate the terms with the variable on one side and the constant

On the other side. Divide the equation by $a$ for the squared term to have a coefficient of $1$ .

Add ${\left(\frac{b}{2}\right)}^2={\left(\frac{4}{2}\right)}^2=2$ on both sides and write the square root of both sides the solve for the variable which is the solution of the equation.

Thus, the discussed the strategies of graphing, factoring and completing the square.