11x^2-35x+10=0

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Solution for 11x^2-35x+10=0 equation:


Simplifying
11x2 + -35x + 10 = 0

Reorder the terms:
10 + -35x + 11x2 = 0

Solving
10 + -35x + 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 + -3.181818182x + x2 = 0

Move the constant term to the right:

Add '-0.9090909091' to each side of the equation.
0.9090909091 + -3.181818182x + -0.9090909091 + x2 = 0 + -0.9090909091

Reorder the terms:
0.9090909091 + -0.9090909091 + -3.181818182x + x2 = 0 + -0.9090909091

Combine like terms: 0.9090909091 + -0.9090909091 = 0.0000000000
0.0000000000 + -3.181818182x + x2 = 0 + -0.9090909091
-3.181818182x + x2 = 0 + -0.9090909091

Combine like terms: 0 + -0.9090909091 = -0.9090909091
-3.181818182x + x2 = -0.9090909091

The x term is -3.181818182x.  Take half its coefficient (-1.590909091).
Square it (2.530991736) and add it to both sides.

Add '2.530991736' to each side of the equation.
-3.181818182x + 2.530991736 + x2 = -0.9090909091 + 2.530991736

Reorder the terms:
2.530991736 + -3.181818182x + x2 = -0.9090909091 + 2.530991736

Combine like terms: -0.9090909091 + 2.530991736 = 1.6219008269
2.530991736 + -3.181818182x + x2 = 1.6219008269

Factor a perfect square on the left side:
(x + -1.590909091)(x + -1.590909091) = 1.6219008269

Calculate the square root of the right side: 1.273538703

Break this problem into two subproblems by setting 
(x + -1.590909091) equal to 1.273538703 and -1.273538703.

Subproblem 1

x + -1.590909091 = 1.273538703 Simplifying x + -1.590909091 = 1.273538703 Reorder the terms: -1.590909091 + x = 1.273538703 Solving -1.590909091 + x = 1.273538703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.590909091' to each side of the equation. -1.590909091 + 1.590909091 + x = 1.273538703 + 1.590909091 Combine like terms: -1.590909091 + 1.590909091 = 0.000000000 0.000000000 + x = 1.273538703 + 1.590909091 x = 1.273538703 + 1.590909091 Combine like terms: 1.273538703 + 1.590909091 = 2.864447794 x = 2.864447794 Simplifying x = 2.864447794

Subproblem 2

x + -1.590909091 = -1.273538703 Simplifying x + -1.590909091 = -1.273538703 Reorder the terms: -1.590909091 + x = -1.273538703 Solving -1.590909091 + x = -1.273538703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.590909091' to each side of the equation. -1.590909091 + 1.590909091 + x = -1.273538703 + 1.590909091 Combine like terms: -1.590909091 + 1.590909091 = 0.000000000 0.000000000 + x = -1.273538703 + 1.590909091 x = -1.273538703 + 1.590909091 Combine like terms: -1.273538703 + 1.590909091 = 0.317370388 x = 0.317370388 Simplifying x = 0.317370388

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.864447794, 0.317370388}

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