x(x+1)=14x+44

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Solution for x(x+1)=14x+44 equation:


Simplifying
x(x + 1) = 14x + 44

Reorder the terms:
x(1 + x) = 14x + 44
(1 * x + x * x) = 14x + 44
(1x + x2) = 14x + 44

Reorder the terms:
1x + x2 = 44 + 14x

Solving
1x + x2 = 44 + 14x

Solving for variable 'x'.

Reorder the terms:
-44 + 1x + -14x + x2 = 44 + 14x + -44 + -14x

Combine like terms: 1x + -14x = -13x
-44 + -13x + x2 = 44 + 14x + -44 + -14x

Reorder the terms:
-44 + -13x + x2 = 44 + -44 + 14x + -14x

Combine like terms: 44 + -44 = 0
-44 + -13x + x2 = 0 + 14x + -14x
-44 + -13x + x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-44 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -13x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + -13x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -13x + x2 = 0 + 44
-13x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
-13x + x2 = 44

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 44 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 44 + 42.25

Combine like terms: 44 + 42.25 = 86.25
42.25 + -13x + x2 = 86.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 86.25

Calculate the square root of the right side: 9.287087811

Break this problem into two subproblems by setting 
(x + -6.5) equal to 9.287087811 and -9.287087811.

Subproblem 1

x + -6.5 = 9.287087811 Simplifying x + -6.5 = 9.287087811 Reorder the terms: -6.5 + x = 9.287087811 Solving -6.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 9.287087811 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 9.287087811 + 6.5 x = 9.287087811 + 6.5 Combine like terms: 9.287087811 + 6.5 = 15.787087811 x = 15.787087811 Simplifying x = 15.787087811

Subproblem 2

x + -6.5 = -9.287087811 Simplifying x + -6.5 = -9.287087811 Reorder the terms: -6.5 + x = -9.287087811 Solving -6.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -9.287087811 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -9.287087811 + 6.5 x = -9.287087811 + 6.5 Combine like terms: -9.287087811 + 6.5 = -2.787087811 x = -2.787087811 Simplifying x = -2.787087811

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.787087811, -2.787087811}

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