1 2x(2 4xx-0 23/x-0 05)=1 44

2 min read Jun 06, 2024

Solving the Equation: 2x(2x-0.23/x-0.05)=1.44

In this article, we will solve the given equation step by step.

The equation is:

2x(2x - 0.23/x - 0.05) = 1.44

Let's start by simplifying the equation. We can begin by evaluating the expression inside the parentheses.

2x(2x - 0.23/x - 0.05) = 2x(2x - (0.23/x + 0.05))

Now, let's expand the equation:

4x² - 0.46x - 0.1x = 1.44

Combine like terms:

4x² - 0.56x - 1.44 = 0

The equation is now in the quadratic form: ax² + bx + c = 0, where a = 4, b = -0.56, and c = -1.44.

We can solve this equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

x = (0.56 ± √((-0.56)² - 4(4)(-1.44))) / (2(4))

x = (0.56 ± √(0.3136 + 23.04)) / 8

x = (0.56 ± √23.3536) / 8

x = (0.56 ± 4.831) / 8

Now, we have two possible solutions:

x = (0.56 + 4.831) / 8 ≈ 0.686

x = (0.56 - 4.831) / 8 ≈ -0.544

The solutions to the equation 2x(2x - 0.23/x - 0.05) = 1.44 are x ≈ 0.686 and x ≈ -0.544.