2x^2+11x+1=180

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Solution for 2x^2+11x+1=180 equation:


Simplifying
2x2 + 11x + 1 = 180

Reorder the terms:
1 + 11x + 2x2 = 180

Solving
1 + 11x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
1 + -180 + 11x + 2x2 = 180 + -180

Combine like terms: 1 + -180 = -179
-179 + 11x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-179 + 11x + 2x2 = 0

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

Divide each side by '2'.
-89.5 + 5.5x + x2 = 0

Move the constant term to the right:

Add '89.5' to each side of the equation.
-89.5 + 5.5x + 89.5 + x2 = 0 + 89.5

Reorder the terms:
-89.5 + 89.5 + 5.5x + x2 = 0 + 89.5

Combine like terms: -89.5 + 89.5 = 0.0
0.0 + 5.5x + x2 = 0 + 89.5
5.5x + x2 = 0 + 89.5

Combine like terms: 0 + 89.5 = 89.5
5.5x + x2 = 89.5

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 89.5 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 89.5 + 7.5625

Combine like terms: 89.5 + 7.5625 = 97.0625
7.5625 + 5.5x + x2 = 97.0625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 97.0625

Calculate the square root of the right side: 9.852030248

Break this problem into two subproblems by setting 
(x + 2.75) equal to 9.852030248 and -9.852030248.

Subproblem 1

x + 2.75 = 9.852030248 Simplifying x + 2.75 = 9.852030248 Reorder the terms: 2.75 + x = 9.852030248 Solving 2.75 + x = 9.852030248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 9.852030248 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 9.852030248 + -2.75 x = 9.852030248 + -2.75 Combine like terms: 9.852030248 + -2.75 = 7.102030248 x = 7.102030248 Simplifying x = 7.102030248

Subproblem 2

x + 2.75 = -9.852030248 Simplifying x + 2.75 = -9.852030248 Reorder the terms: 2.75 + x = -9.852030248 Solving 2.75 + x = -9.852030248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -9.852030248 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -9.852030248 + -2.75 x = -9.852030248 + -2.75 Combine like terms: -9.852030248 + -2.75 = -12.602030248 x = -12.602030248 Simplifying x = -12.602030248

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.102030248, -12.602030248}

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