(x-4)(x+14)=44

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Solution for (x-4)(x+14)=44 equation:


Simplifying
(x + -4)(x + 14) = 44

Reorder the terms:
(-4 + x)(x + 14) = 44

Reorder the terms:
(-4 + x)(14 + x) = 44

Multiply (-4 + x) * (14 + x)
(-4(14 + x) + x(14 + x)) = 44
((14 * -4 + x * -4) + x(14 + x)) = 44
((-56 + -4x) + x(14 + x)) = 44
(-56 + -4x + (14 * x + x * x)) = 44
(-56 + -4x + (14x + x2)) = 44

Combine like terms: -4x + 14x = 10x
(-56 + 10x + x2) = 44

Solving
-56 + 10x + x2 = 44

Solving for variable 'x'.

Reorder the terms:
-56 + -44 + 10x + x2 = 44 + -44

Combine like terms: -56 + -44 = -100
-100 + 10x + x2 = 44 + -44

Combine like terms: 44 + -44 = 0
-100 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 10x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 10x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 10x + x2 = 0 + 100
10x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
10x + x2 = 100

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 100 + 25

Reorder the terms:
25 + 10x + x2 = 100 + 25

Combine like terms: 100 + 25 = 125
25 + 10x + x2 = 125

Factor a perfect square on the left side:
(x + 5)(x + 5) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(x + 5) equal to 11.180339887 and -11.180339887.

Subproblem 1

x + 5 = 11.180339887 Simplifying x + 5 = 11.180339887 Reorder the terms: 5 + x = 11.180339887 Solving 5 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + x = 11.180339887 + -5 x = 11.180339887 + -5 Combine like terms: 11.180339887 + -5 = 6.180339887 x = 6.180339887 Simplifying x = 6.180339887

Subproblem 2

x + 5 = -11.180339887 Simplifying x + 5 = -11.180339887 Reorder the terms: 5 + x = -11.180339887 Solving 5 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + x = -11.180339887 + -5 x = -11.180339887 + -5 Combine like terms: -11.180339887 + -5 = -16.180339887 x = -16.180339887 Simplifying x = -16.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.180339887, -16.180339887}

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