2x^2+11x-294=0

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Solution for 2x^2+11x-294=0 equation: 


Simplifying
2x2 + 11x + -294 = 0

Reorder the terms:
-294 + 11x + 2x2 = 0

Solving
-294 + 11x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-147 + 5.5x + x2 = 0

Move the constant term to the right:

Add '147' to each side of the equation.
-147 + 5.5x + 147 + x2 = 0 + 147

Reorder the terms:
-147 + 147 + 5.5x + x2 = 0 + 147

Combine like terms: -147 + 147 = 0
0 + 5.5x + x2 = 0 + 147
5.5x + x2 = 0 + 147

Combine like terms: 0 + 147 = 147
5.5x + x2 = 147

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 = 147 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 147 + 7.5625

Combine like terms: 147 + 7.5625 = 154.5625
7.5625 + 5.5x + x2 = 154.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 154.5625

Calculate the square root of the right side: 12.432316759

Break this problem into two subproblems by setting 
(x + 2.75) equal to 12.432316759 and -12.432316759.


Subproblem 1
x + 2.75 = 12.432316759

Simplifying
x + 2.75 = 12.432316759

Reorder the terms:
2.75 + x = 12.432316759

Solving
2.75 + x = 12.432316759

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 = 12.432316759 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 12.432316759 + -2.75
x = 12.432316759 + -2.75

Combine like terms: 12.432316759 + -2.75 = 9.682316759
x = 9.682316759

Simplifying
x = 9.682316759


Subproblem 2
x + 2.75 = -12.432316759

Simplifying
x + 2.75 = -12.432316759

Reorder the terms:
2.75 + x = -12.432316759

Solving
2.75 + x = -12.432316759

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 = -12.432316759 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -12.432316759 + -2.75
x = -12.432316759 + -2.75

Combine like terms: -12.432316759 + -2.75 = -15.182316759
x = -15.182316759

Simplifying
x = -15.182316759


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.682316759, -15.182316759}

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