44=(2x+1)(x+3)

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Solution for 44=(2x+1)(x+3) equation:


Simplifying
44 = (2x + 1)(x + 3)

Reorder the terms:
44 = (1 + 2x)(x + 3)

Reorder the terms:
44 = (1 + 2x)(3 + x)

Multiply (1 + 2x) * (3 + x)
44 = (1(3 + x) + 2x * (3 + x))
44 = ((3 * 1 + x * 1) + 2x * (3 + x))
44 = ((3 + 1x) + 2x * (3 + x))
44 = (3 + 1x + (3 * 2x + x * 2x))
44 = (3 + 1x + (6x + 2x2))

Combine like terms: 1x + 6x = 7x
44 = (3 + 7x + 2x2)

Solving
44 = 3 + 7x + 2x2

Solving for variable 'x'.

Combine like terms: 44 + -3 = 41
41 + -7x + -2x2 = 3 + 7x + 2x2 + -3 + -7x + -2x2

Reorder the terms:
41 + -7x + -2x2 = 3 + -3 + 7x + -7x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
41 + -7x + -2x2 = 0 + 7x + -7x + 2x2 + -2x2
41 + -7x + -2x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
41 + -7x + -2x2 = 0 + 2x2 + -2x2
41 + -7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
41 + -7x + -2x2 = 0

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

Divide each side by '-2'.
-20.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '20.5' to each side of the equation.
-20.5 + 3.5x + 20.5 + x2 = 0 + 20.5

Reorder the terms:
-20.5 + 20.5 + 3.5x + x2 = 0 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + 3.5x + x2 = 0 + 20.5
3.5x + x2 = 0 + 20.5

Combine like terms: 0 + 20.5 = 20.5
3.5x + x2 = 20.5

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 = 20.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 20.5 + 3.0625

Combine like terms: 20.5 + 3.0625 = 23.5625
3.0625 + 3.5x + x2 = 23.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 23.5625

Calculate the square root of the right side: 4.85412196

Break this problem into two subproblems by setting 
(x + 1.75) equal to 4.85412196 and -4.85412196.

Subproblem 1

x + 1.75 = 4.85412196 Simplifying x + 1.75 = 4.85412196 Reorder the terms: 1.75 + x = 4.85412196 Solving 1.75 + x = 4.85412196 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 = 4.85412196 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.85412196 + -1.75 x = 4.85412196 + -1.75 Combine like terms: 4.85412196 + -1.75 = 3.10412196 x = 3.10412196 Simplifying x = 3.10412196

Subproblem 2

x + 1.75 = -4.85412196 Simplifying x + 1.75 = -4.85412196 Reorder the terms: 1.75 + x = -4.85412196 Solving 1.75 + x = -4.85412196 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 = -4.85412196 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.85412196 + -1.75 x = -4.85412196 + -1.75 Combine like terms: -4.85412196 + -1.75 = -6.60412196 x = -6.60412196 Simplifying x = -6.60412196

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.10412196, -6.60412196}

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