x=(2x+1)(x-3)-4x+1

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Solution for x=(2x+1)(x-3)-4x+1 equation:


Simplifying
x = (2x + 1)(x + -3) + -4x + 1

Reorder the terms:
x = (1 + 2x)(x + -3) + -4x + 1

Reorder the terms:
x = (1 + 2x)(-3 + x) + -4x + 1

Multiply (1 + 2x) * (-3 + x)
x = (1(-3 + x) + 2x * (-3 + x)) + -4x + 1
x = ((-3 * 1 + x * 1) + 2x * (-3 + x)) + -4x + 1
x = ((-3 + 1x) + 2x * (-3 + x)) + -4x + 1
x = (-3 + 1x + (-3 * 2x + x * 2x)) + -4x + 1
x = (-3 + 1x + (-6x + 2x2)) + -4x + 1

Combine like terms: 1x + -6x = -5x
x = (-3 + -5x + 2x2) + -4x + 1

Reorder the terms:
x = -3 + 1 + -5x + -4x + 2x2

Combine like terms: -3 + 1 = -2
x = -2 + -5x + -4x + 2x2

Combine like terms: -5x + -4x = -9x
x = -2 + -9x + 2x2

Solving
x = -2 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + x + 9x + -2x2 = -2 + -9x + 2x2 + 2 + 9x + -2x2

Combine like terms: x + 9x = 10x
2 + 10x + -2x2 = -2 + -9x + 2x2 + 2 + 9x + -2x2

Reorder the terms:
2 + 10x + -2x2 = -2 + 2 + -9x + 9x + 2x2 + -2x2

Combine like terms: -2 + 2 = 0
2 + 10x + -2x2 = 0 + -9x + 9x + 2x2 + -2x2
2 + 10x + -2x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
2 + 10x + -2x2 = 0 + 2x2 + -2x2
2 + 10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + 10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 5x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + -1x2 = 0 Solving 1 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x + x2 = 0 + 1 -5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5x + x2 = 1 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 1 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1 + 6.25 Combine like terms: 1 + 6.25 = 7.25 6.25 + -5x + x2 = 7.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -2.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

x + -2.5 = 2.692582404 Simplifying x + -2.5 = 2.692582404 Reorder the terms: -2.5 + x = 2.692582404 Solving -2.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.692582404 + 2.5 x = 2.692582404 + 2.5 Combine like terms: 2.692582404 + 2.5 = 5.192582404 x = 5.192582404 Simplifying x = 5.192582404

Subproblem 2

x + -2.5 = -2.692582404 Simplifying x + -2.5 = -2.692582404 Reorder the terms: -2.5 + x = -2.692582404 Solving -2.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.692582404 + 2.5 x = -2.692582404 + 2.5 Combine like terms: -2.692582404 + 2.5 = -0.192582404 x = -0.192582404 Simplifying x = -0.192582404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.192582404, -0.192582404}

Solution

x = {5.192582404, -0.192582404}

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