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(3x-1)2-3(2x+3)2+42=2x(-x-5)-(x-1)2

2 min read Jun 16, 2024
(3x-1)2-3(2x+3)2+42=2x(-x-5)-(x-1)2

Solving the Equation (3x-1)2-3(2x+3)2+42=2x(-x-5)-(x-1)2

This article will walk through the steps to solve the equation (3x-1)2-3(2x+3)2+42=2x(-x-5)-(x-1)2.

Step 1: Expanding the Equations

First, we need to expand the equations on both sides. Remember the formula (a+b)2 = a2 + 2ab + b2.

  • Left Side:
    • (3x-1)2 = 9x2 - 6x + 1
    • 3(2x+3)2 = 3(4x2 + 12x + 9) = 12x2 + 36x + 27
  • Right Side:
    • 2x(-x-5) = -2x2 - 10x
    • (x-1)2 = x2 - 2x + 1

Now, the equation becomes: 9x2 - 6x + 1 - 12x2 - 36x - 27 + 42 = -2x2 - 10x - x2 + 2x - 1

Step 2: Combining Like Terms

Combine the like terms on both sides of the equation.

  • Left Side: -3x2 - 42x + 16
  • Right Side: -3x2 - 8x - 1

The equation now is: -3x2 - 42x + 16 = -3x2 - 8x - 1

Step 3: Isolating the Variable

  • Add 3x2 to both sides to eliminate the x2 terms: -3x2 - 42x + 16 + 3x2 = -3x2 - 8x - 1 + 3x2 -42x + 16 = -8x - 1
  • Add 8x to both sides: -42x + 16 + 8x = -8x - 1 + 8x -34x + 16 = -1
  • Subtract 16 from both sides: -34x + 16 - 16 = -1 - 16 -34x = -17

Step 4: Solving for x

Divide both sides by -34 to isolate x: -34x / -34 = -17 / -34 x = 1/2

Therefore, the solution to the equation (3x-1)2-3(2x+3)2+42=2x(-x-5)-(x-1)2 is x = 1/2.

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