x(4x+44)=153

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Solution for x(4x+44)=153 equation:


Simplifying
x(4x + 44) = 153

Reorder the terms:
x(44 + 4x) = 153
(44 * x + 4x * x) = 153
(44x + 4x2) = 153

Solving
44x + 4x2 = 153

Solving for variable 'x'.

Reorder the terms:
-153 + 44x + 4x2 = 153 + -153

Combine like terms: 153 + -153 = 0
-153 + 44x + 4x2 = 0

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

Divide each side by '4'.
-38.25 + 11x + x2 = 0

Move the constant term to the right:

Add '38.25' to each side of the equation.
-38.25 + 11x + 38.25 + x2 = 0 + 38.25

Reorder the terms:
-38.25 + 38.25 + 11x + x2 = 0 + 38.25

Combine like terms: -38.25 + 38.25 = 0.00
0.00 + 11x + x2 = 0 + 38.25
11x + x2 = 0 + 38.25

Combine like terms: 0 + 38.25 = 38.25
11x + x2 = 38.25

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 38.25 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 38.25 + 30.25

Combine like terms: 38.25 + 30.25 = 68.5
30.25 + 11x + x2 = 68.5

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 68.5

Calculate the square root of the right side: 8.276472679

Break this problem into two subproblems by setting 
(x + 5.5) equal to 8.276472679 and -8.276472679.

Subproblem 1

x + 5.5 = 8.276472679 Simplifying x + 5.5 = 8.276472679 Reorder the terms: 5.5 + x = 8.276472679 Solving 5.5 + x = 8.276472679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 8.276472679 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 8.276472679 + -5.5 x = 8.276472679 + -5.5 Combine like terms: 8.276472679 + -5.5 = 2.776472679 x = 2.776472679 Simplifying x = 2.776472679

Subproblem 2

x + 5.5 = -8.276472679 Simplifying x + 5.5 = -8.276472679 Reorder the terms: 5.5 + x = -8.276472679 Solving 5.5 + x = -8.276472679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -8.276472679 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -8.276472679 + -5.5 x = -8.276472679 + -5.5 Combine like terms: -8.276472679 + -5.5 = -13.776472679 x = -13.776472679 Simplifying x = -13.776472679

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.776472679, -13.776472679}

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