2x^2+11x+2=0

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


Simplifying
2x2 + 11x + 2 = 0

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

Solving
2 + 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'.
1 + 5.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 5.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 5.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5.5x + x2 = 0 + -1
5.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
5.5x + x2 = -1

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 = -1 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -1 + 7.5625

Combine like terms: -1 + 7.5625 = 6.5625
7.5625 + 5.5x + x2 = 6.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(x + 2.75) equal to 2.561737691 and -2.561737691.

Subproblem 1

x + 2.75 = 2.561737691 Simplifying x + 2.75 = 2.561737691 Reorder the terms: 2.75 + x = 2.561737691 Solving 2.75 + x = 2.561737691 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 = 2.561737691 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 2.561737691 + -2.75 x = 2.561737691 + -2.75 Combine like terms: 2.561737691 + -2.75 = -0.188262309 x = -0.188262309 Simplifying x = -0.188262309

Subproblem 2

x + 2.75 = -2.561737691 Simplifying x + 2.75 = -2.561737691 Reorder the terms: 2.75 + x = -2.561737691 Solving 2.75 + x = -2.561737691 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 = -2.561737691 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -2.561737691 + -2.75 x = -2.561737691 + -2.75 Combine like terms: -2.561737691 + -2.75 = -5.311737691 x = -5.311737691 Simplifying x = -5.311737691

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.188262309, -5.311737691}

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