11x^2-2x-15=0

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Solution for 11x^2-2x-15=0 equation:


Simplifying
11x2 + -2x + -15 = 0

Reorder the terms:
-15 + -2x + 11x2 = 0

Solving
-15 + -2x + 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'.
-1.363636364 + -0.1818181818x + x2 = 0

Move the constant term to the right:

Add '1.363636364' to each side of the equation.
-1.363636364 + -0.1818181818x + 1.363636364 + x2 = 0 + 1.363636364

Reorder the terms:
-1.363636364 + 1.363636364 + -0.1818181818x + x2 = 0 + 1.363636364

Combine like terms: -1.363636364 + 1.363636364 = 0.000000000
0.000000000 + -0.1818181818x + x2 = 0 + 1.363636364
-0.1818181818x + x2 = 0 + 1.363636364

Combine like terms: 0 + 1.363636364 = 1.363636364
-0.1818181818x + x2 = 1.363636364

The x term is -0.1818181818x.  Take half its coefficient (-0.0909090909).
Square it (0.008264462808) and add it to both sides.

Add '0.008264462808' to each side of the equation.
-0.1818181818x + 0.008264462808 + x2 = 1.363636364 + 0.008264462808

Reorder the terms:
0.008264462808 + -0.1818181818x + x2 = 1.363636364 + 0.008264462808

Combine like terms: 1.363636364 + 0.008264462808 = 1.371900826808
0.008264462808 + -0.1818181818x + x2 = 1.371900826808

Factor a perfect square on the left side:
(x + -0.0909090909)(x + -0.0909090909) = 1.371900826808

Calculate the square root of the right side: 1.171281703

Break this problem into two subproblems by setting 
(x + -0.0909090909) equal to 1.171281703 and -1.171281703.

Subproblem 1

x + -0.0909090909 = 1.171281703 Simplifying x + -0.0909090909 = 1.171281703 Reorder the terms: -0.0909090909 + x = 1.171281703 Solving -0.0909090909 + x = 1.171281703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = 1.171281703 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = 1.171281703 + 0.0909090909 x = 1.171281703 + 0.0909090909 Combine like terms: 1.171281703 + 0.0909090909 = 1.2621907939 x = 1.2621907939 Simplifying x = 1.2621907939

Subproblem 2

x + -0.0909090909 = -1.171281703 Simplifying x + -0.0909090909 = -1.171281703 Reorder the terms: -0.0909090909 + x = -1.171281703 Solving -0.0909090909 + x = -1.171281703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = -1.171281703 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = -1.171281703 + 0.0909090909 x = -1.171281703 + 0.0909090909 Combine like terms: -1.171281703 + 0.0909090909 = -1.0803726121 x = -1.0803726121 Simplifying x = -1.0803726121

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2621907939, -1.0803726121}

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