Resolve the Equation: 5x² + 7x + 9 = (2x-1)(2x+1)

Question

Solve the following equation:

^{$5x^{2}+7x+9=(2x-1)(2x+1)$}

00:00 Solve

00:11 Let's use the abbreviated multiplication formulas

00:35 Open the parentheses, calculate 2 squared

00:44 Arrange the equation so that the right side equals 0

01:00 Collect terms

01:11 Use the abbreviated multiplication formulas and find two numbers

01:15 whose sum equals 7

01:19 and their product equals 10

01:24 These are the matching numbers

01:31 Find the possible solutions that make the equation equal zero

01:45 And this is the solution to the problem

Let's begin by focusing on the right side of the equation:

(2x-1)(2x+1)

We must first open the parentheses whilst multiplying all the terms as needed:

2x*2x+2x*1+-1*2x+-1*1

4x^2+2x-2x-1
4x^2-1

Let's now return to the original equation, and move all terms to the same side.

5X^2+7x+9=4X^2-1
5X^2-4X^2+7x+9+1=0
X^2+7X+10=0

We are left with a simple quadratic equation, which can be solved using any method we desire (factoring or the quadratic formula).

Therefore the final solution is:

X= -2,-5

2-,5-