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(x+10)(x-4)=(x+2)^2

less than a minute read Jun 16, 2024
(x+10)(x-4)=(x+2)^2

Solving the Equation: (x+10)(x-4) = (x+2)^2

This equation presents a quadratic equation that can be solved using algebraic manipulation. Let's break down the steps:

1. Expand both sides of the equation

  • Left side: (x+10)(x-4) = x² - 4x + 10x - 40 = x² + 6x - 40
  • Right side: (x+2)² = (x+2)(x+2) = x² + 2x + 2x + 4 = x² + 4x + 4

Now, the equation becomes: x² + 6x - 40 = x² + 4x + 4

2. Simplify the equation

Subtract x² from both sides: 6x - 40 = 4x + 4 Subtract 4x from both sides: 2x - 40 = 4 Add 40 to both sides: 2x = 44

3. Solve for x

Divide both sides by 2: x = 22

Conclusion

Therefore, the solution to the equation (x+10)(x-4) = (x+2)² is x = 22.

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