1=11x^2+2x

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Solution for 1=11x^2+2x equation:


Simplifying
1 = 11x2 + 2x

Reorder the terms:
1 = 2x + 11x2

Solving
1 = 2x + 11x2

Solving for variable 'x'.

Reorder the terms:
1 + -2x + -11x2 = 2x + -2x + 11x2 + -11x2

Combine like terms: 2x + -2x = 0
1 + -2x + -11x2 = 0 + 11x2 + -11x2
1 + -2x + -11x2 = 11x2 + -11x2

Combine like terms: 11x2 + -11x2 = 0
1 + -2x + -11x2 = 0

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

Divide each side by '-11'.
-0.09090909091 + 0.1818181818x + x2 = 0

Move the constant term to the right:

Add '0.09090909091' to each side of the equation.
-0.09090909091 + 0.1818181818x + 0.09090909091 + x2 = 0 + 0.09090909091

Reorder the terms:
-0.09090909091 + 0.09090909091 + 0.1818181818x + x2 = 0 + 0.09090909091

Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000
0.00000000000 + 0.1818181818x + x2 = 0 + 0.09090909091
0.1818181818x + x2 = 0 + 0.09090909091

Combine like terms: 0 + 0.09090909091 = 0.09090909091
0.1818181818x + x2 = 0.09090909091

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 = 0.09090909091 + 0.008264462808

Reorder the terms:
0.008264462808 + 0.1818181818x + x2 = 0.09090909091 + 0.008264462808

Combine like terms: 0.09090909091 + 0.008264462808 = 0.099173553718
0.008264462808 + 0.1818181818x + x2 = 0.099173553718

Factor a perfect square on the left side:
(x + 0.0909090909)(x + 0.0909090909) = 0.099173553718

Calculate the square root of the right side: 0.314918329

Break this problem into two subproblems by setting 
(x + 0.0909090909) equal to 0.314918329 and -0.314918329.

Subproblem 1

x + 0.0909090909 = 0.314918329 Simplifying x + 0.0909090909 = 0.314918329 Reorder the terms: 0.0909090909 + x = 0.314918329 Solving 0.0909090909 + x = 0.314918329 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 = 0.314918329 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 0.314918329 + -0.0909090909 x = 0.314918329 + -0.0909090909 Combine like terms: 0.314918329 + -0.0909090909 = 0.2240092381 x = 0.2240092381 Simplifying x = 0.2240092381

Subproblem 2

x + 0.0909090909 = -0.314918329 Simplifying x + 0.0909090909 = -0.314918329 Reorder the terms: 0.0909090909 + x = -0.314918329 Solving 0.0909090909 + x = -0.314918329 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 = -0.314918329 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -0.314918329 + -0.0909090909 x = -0.314918329 + -0.0909090909 Combine like terms: -0.314918329 + -0.0909090909 = -0.4058274199 x = -0.4058274199 Simplifying x = -0.4058274199

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2240092381, -0.4058274199}

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