(2x+1)(x-4)=14

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Solution for (2x+1)(x-4)=14 equation:


Simplifying
(2x + 1)(x + -4) = 14

Reorder the terms:
(1 + 2x)(x + -4) = 14

Reorder the terms:
(1 + 2x)(-4 + x) = 14

Multiply (1 + 2x) * (-4 + x)
(1(-4 + x) + 2x * (-4 + x)) = 14
((-4 * 1 + x * 1) + 2x * (-4 + x)) = 14
((-4 + 1x) + 2x * (-4 + x)) = 14
(-4 + 1x + (-4 * 2x + x * 2x)) = 14
(-4 + 1x + (-8x + 2x2)) = 14

Combine like terms: 1x + -8x = -7x
(-4 + -7x + 2x2) = 14

Solving
-4 + -7x + 2x2 = 14

Solving for variable 'x'.

Reorder the terms:
-4 + -14 + -7x + 2x2 = 14 + -14

Combine like terms: -4 + -14 = -18
-18 + -7x + 2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-18 + -7x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-9 + -3.5x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -3.5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -3.5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -3.5x + x2 = 0 + 9
-3.5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-3.5x + x2 = 9

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 9 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 9 + 3.0625

Combine like terms: 9 + 3.0625 = 12.0625
3.0625 + -3.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + -1.75) equal to 3.473110997 and -3.473110997.

Subproblem 1

x + -1.75 = 3.473110997 Simplifying x + -1.75 = 3.473110997 Reorder the terms: -1.75 + x = 3.473110997 Solving -1.75 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.473110997 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.473110997 + 1.75 x = 3.473110997 + 1.75 Combine like terms: 3.473110997 + 1.75 = 5.223110997 x = 5.223110997 Simplifying x = 5.223110997

Subproblem 2

x + -1.75 = -3.473110997 Simplifying x + -1.75 = -3.473110997 Reorder the terms: -1.75 + x = -3.473110997 Solving -1.75 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.473110997 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.473110997 + 1.75 x = -3.473110997 + 1.75 Combine like terms: -3.473110997 + 1.75 = -1.723110997 x = -1.723110997 Simplifying x = -1.723110997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.223110997, -1.723110997}

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