2x^2+11x=22

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Solution for 2x^2+11x=22 equation:


Simplifying
2x2 + 11x = 22

Reorder the terms:
11x + 2x2 = 22

Solving
11x + 2x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + 11x + 2x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 11x + 2x2 = 0

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

Divide each side by '2'.
-11 + 5.5x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 5.5x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 5.5x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 5.5x + x2 = 0 + 11
5.5x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
5.5x + x2 = 11

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 = 11 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 11 + 7.5625

Combine like terms: 11 + 7.5625 = 18.5625
7.5625 + 5.5x + x2 = 18.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 18.5625

Calculate the square root of the right side: 4.308421985

Break this problem into two subproblems by setting 
(x + 2.75) equal to 4.308421985 and -4.308421985.

Subproblem 1

x + 2.75 = 4.308421985 Simplifying x + 2.75 = 4.308421985 Reorder the terms: 2.75 + x = 4.308421985 Solving 2.75 + x = 4.308421985 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 = 4.308421985 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.308421985 + -2.75 x = 4.308421985 + -2.75 Combine like terms: 4.308421985 + -2.75 = 1.558421985 x = 1.558421985 Simplifying x = 1.558421985

Subproblem 2

x + 2.75 = -4.308421985 Simplifying x + 2.75 = -4.308421985 Reorder the terms: 2.75 + x = -4.308421985 Solving 2.75 + x = -4.308421985 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 = -4.308421985 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.308421985 + -2.75 x = -4.308421985 + -2.75 Combine like terms: -4.308421985 + -2.75 = -7.058421985 x = -7.058421985 Simplifying x = -7.058421985

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.558421985, -7.058421985}

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