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

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


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

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

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

Combine like terms: 3x + -1x = 2x
-4 + 2x = 2(x + 1) * 2x + 1

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

Reorder the terms for easier multiplication:
-4 + 2x = 2 * 2x(1 + x) + 1

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

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

Solving
-4 + 2x = 1 + 4x + 4x2

Solving for variable 'x'.

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

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

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

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

Combine like terms: 1 + -1 = 0
-5 + -2x + -4x2 = 0 + 4x + -4x + 4x2 + -4x2
-5 + -2x + -4x2 = 4x + -4x + 4x2 + -4x2

Combine like terms: 4x + -4x = 0
-5 + -2x + -4x2 = 0 + 4x2 + -4x2
-5 + -2x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5 + -2x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 2x + 4x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(5 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 2x + 4x2 = 0 Solving 5 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.5x + x2 = 0 + -1.25 0.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.5x + x2 = -1.25 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -1.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -1.25 + 0.0625 Combine like terms: -1.25 + 0.0625 = -1.1875 0.0625 + 0.5x + x2 = -1.1875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -1.1875 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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