(2v-1)^2=26-4v

Jasonbradley

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Jun 16, 2024

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Solving the Quadratic Equation: (2v - 1)^2 = 26 - 4v

This article will guide you through the steps involved in solving the quadratic equation (2v - 1)^2 = 26 - 4v.

Understanding the Equation

The equation (2v - 1)^2 = 26 - 4v is a quadratic equation. This is because the highest power of the variable 'v' is 2. To solve this, we need to manipulate the equation to get it in the standard quadratic form: ax² + bx + c = 0.

Solving the Equation

1. Expand the Square: Start by expanding the left side of the equation: (2v - 1)² = (2v - 1)(2v - 1) = 4v² - 4v + 1

2. Rearrange the Equation: Now move all the terms to the left side of the equation: 4v² - 4v + 1 = 26 - 4v 4v² - 4v + 4v + 1 - 26 = 0 4v² - 25 = 0

3. Solve for 'v': We can now solve this quadratic equation in a few ways:

   • Factoring: The equation can be factored as: (2v + 5)(2v - 5) = 0. This gives us two possible solutions:
     • 2v + 5 = 0 => v = -5/2
     • 2v - 5 = 0 => v = 5/2
   • Quadratic Formula: The quadratic formula can be used to find the solutions of any quadratic equation of the form ax² + bx + c = 0. The formula is: v = (-b ± √(b² - 4ac)) / 2a In our equation, a = 4, b = 0, and c = -25. Plugging these values into the formula, we get: v = (0 ± √(0² - 4 * 4 * -25)) / (2 * 4) v = ± √(400) / 8 v = ± 20 / 8 v = ± 5/2

Solutions

Therefore, the solutions to the quadratic equation (2v - 1)² = 26 - 4v are v = 5/2 and v = -5/2.