4x^2+114x+11=180

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Solution for 4x^2+114x+11=180 equation:


Simplifying
4x2 + 114x + 11 = 180

Reorder the terms:
11 + 114x + 4x2 = 180

Solving
11 + 114x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
11 + -180 + 114x + 4x2 = 180 + -180

Combine like terms: 11 + -180 = -169
-169 + 114x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-169 + 114x + 4x2 = 0

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

Divide each side by '4'.
-42.25 + 28.5x + x2 = 0

Move the constant term to the right:

Add '42.25' to each side of the equation.
-42.25 + 28.5x + 42.25 + x2 = 0 + 42.25

Reorder the terms:
-42.25 + 42.25 + 28.5x + x2 = 0 + 42.25

Combine like terms: -42.25 + 42.25 = 0.00
0.00 + 28.5x + x2 = 0 + 42.25
28.5x + x2 = 0 + 42.25

Combine like terms: 0 + 42.25 = 42.25
28.5x + x2 = 42.25

The x term is 28.5x.  Take half its coefficient (14.25).
Square it (203.0625) and add it to both sides.

Add '203.0625' to each side of the equation.
28.5x + 203.0625 + x2 = 42.25 + 203.0625

Reorder the terms:
203.0625 + 28.5x + x2 = 42.25 + 203.0625

Combine like terms: 42.25 + 203.0625 = 245.3125
203.0625 + 28.5x + x2 = 245.3125

Factor a perfect square on the left side:
(x + 14.25)(x + 14.25) = 245.3125

Calculate the square root of the right side: 15.662455108

Break this problem into two subproblems by setting 
(x + 14.25) equal to 15.662455108 and -15.662455108.

Subproblem 1

x + 14.25 = 15.662455108 Simplifying x + 14.25 = 15.662455108 Reorder the terms: 14.25 + x = 15.662455108 Solving 14.25 + x = 15.662455108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.25' to each side of the equation. 14.25 + -14.25 + x = 15.662455108 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + x = 15.662455108 + -14.25 x = 15.662455108 + -14.25 Combine like terms: 15.662455108 + -14.25 = 1.412455108 x = 1.412455108 Simplifying x = 1.412455108

Subproblem 2

x + 14.25 = -15.662455108 Simplifying x + 14.25 = -15.662455108 Reorder the terms: 14.25 + x = -15.662455108 Solving 14.25 + x = -15.662455108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.25' to each side of the equation. 14.25 + -14.25 + x = -15.662455108 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + x = -15.662455108 + -14.25 x = -15.662455108 + -14.25 Combine like terms: -15.662455108 + -14.25 = -29.912455108 x = -29.912455108 Simplifying x = -29.912455108

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.412455108, -29.912455108}

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