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(x-3)(2x+1)=x(x+5) Answer

2 min read Jun 17, 2024
(x-3)(2x+1)=x(x+5) Answer

Solving the Equation (x-3)(2x+1) = x(x+5)

This equation involves expanding brackets and rearranging terms to solve for x. Here's how to solve it step-by-step:

1. Expand the brackets:

  • On the left-hand side: (x-3)(2x+1) = 2x² + x - 6x - 3 = 2x² - 5x - 3
  • On the right-hand side: x(x+5) = x² + 5x

Now the equation becomes: 2x² - 5x - 3 = x² + 5x

2. Rearrange terms to get a standard quadratic equation:

  • Subtract x² from both sides: x² - 5x - 3 = 5x
  • Subtract 5x from both sides: x² - 10x - 3 = 0

3. Solve the quadratic equation:

This quadratic equation can be solved using the quadratic formula:

  • x = [-b ± √(b² - 4ac)] / 2a

Where:

  • a = 1 (coefficient of x²)
  • b = -10 (coefficient of x)
  • c = -3 (constant term)

4. Substitute the values and calculate:

  • x = [10 ± √((-10)² - 4 * 1 * -3)] / (2 * 1)
  • x = [10 ± √(112)] / 2
  • x = [10 ± 4√7] / 2

5. Simplify the solutions:

  • x = 5 ± 2√7

Therefore, the solutions to the equation (x-3)(2x+1) = x(x+5) are x = 5 + 2√7 and x = 5 - 2√7.

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