11x^2-31x-10=0

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Solution for 11x^2-31x-10=0 equation:


Simplifying
11x2 + -31x + -10 = 0

Reorder the terms:
-10 + -31x + 11x2 = 0

Solving
-10 + -31x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-0.9090909091 + -2.818181818x + x2 = 0

Move the constant term to the right:

Add '0.9090909091' to each side of the equation.
-0.9090909091 + -2.818181818x + 0.9090909091 + x2 = 0 + 0.9090909091

Reorder the terms:
-0.9090909091 + 0.9090909091 + -2.818181818x + x2 = 0 + 0.9090909091

Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000
0.0000000000 + -2.818181818x + x2 = 0 + 0.9090909091
-2.818181818x + x2 = 0 + 0.9090909091

Combine like terms: 0 + 0.9090909091 = 0.9090909091
-2.818181818x + x2 = 0.9090909091

The x term is -2.818181818x.  Take half its coefficient (-1.409090909).
Square it (1.985537190) and add it to both sides.

Add '1.985537190' to each side of the equation.
-2.818181818x + 1.985537190 + x2 = 0.9090909091 + 1.985537190

Reorder the terms:
1.985537190 + -2.818181818x + x2 = 0.9090909091 + 1.985537190

Combine like terms: 0.9090909091 + 1.985537190 = 2.8946280991
1.985537190 + -2.818181818x + x2 = 2.8946280991

Factor a perfect square on the left side:
(x + -1.409090909)(x + -1.409090909) = 2.8946280991

Calculate the square root of the right side: 1.701360661

Break this problem into two subproblems by setting 
(x + -1.409090909) equal to 1.701360661 and -1.701360661.

Subproblem 1

x + -1.409090909 = 1.701360661 Simplifying x + -1.409090909 = 1.701360661 Reorder the terms: -1.409090909 + x = 1.701360661 Solving -1.409090909 + x = 1.701360661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.409090909' to each side of the equation. -1.409090909 + 1.409090909 + x = 1.701360661 + 1.409090909 Combine like terms: -1.409090909 + 1.409090909 = 0.000000000 0.000000000 + x = 1.701360661 + 1.409090909 x = 1.701360661 + 1.409090909 Combine like terms: 1.701360661 + 1.409090909 = 3.11045157 x = 3.11045157 Simplifying x = 3.11045157

Subproblem 2

x + -1.409090909 = -1.701360661 Simplifying x + -1.409090909 = -1.701360661 Reorder the terms: -1.409090909 + x = -1.701360661 Solving -1.409090909 + x = -1.701360661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.409090909' to each side of the equation. -1.409090909 + 1.409090909 + x = -1.701360661 + 1.409090909 Combine like terms: -1.409090909 + 1.409090909 = 0.000000000 0.000000000 + x = -1.701360661 + 1.409090909 x = -1.701360661 + 1.409090909 Combine like terms: -1.701360661 + 1.409090909 = -0.292269752 x = -0.292269752 Simplifying x = -0.292269752

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.11045157, -0.292269752}

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