11x^2-8x=97

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Solution for 11x^2-8x=97 equation:


Simplifying
11x2 + -8x = 97

Reorder the terms:
-8x + 11x2 = 97

Solving
-8x + 11x2 = 97

Solving for variable 'x'.

Reorder the terms:
-97 + -8x + 11x2 = 97 + -97

Combine like terms: 97 + -97 = 0
-97 + -8x + 11x2 = 0

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

Divide each side by '11'.
-8.818181818 + -0.7272727273x + x2 = 0

Move the constant term to the right:

Add '8.818181818' to each side of the equation.
-8.818181818 + -0.7272727273x + 8.818181818 + x2 = 0 + 8.818181818

Reorder the terms:
-8.818181818 + 8.818181818 + -0.7272727273x + x2 = 0 + 8.818181818

Combine like terms: -8.818181818 + 8.818181818 = 0.000000000
0.000000000 + -0.7272727273x + x2 = 0 + 8.818181818
-0.7272727273x + x2 = 0 + 8.818181818

Combine like terms: 0 + 8.818181818 = 8.818181818
-0.7272727273x + x2 = 8.818181818

The x term is -0.7272727273x.  Take half its coefficient (-0.3636363637).
Square it (0.1322314050) and add it to both sides.

Add '0.1322314050' to each side of the equation.
-0.7272727273x + 0.1322314050 + x2 = 8.818181818 + 0.1322314050

Reorder the terms:
0.1322314050 + -0.7272727273x + x2 = 8.818181818 + 0.1322314050

Combine like terms: 8.818181818 + 0.1322314050 = 8.950413223
0.1322314050 + -0.7272727273x + x2 = 8.950413223

Factor a perfect square on the left side:
(x + -0.3636363637)(x + -0.3636363637) = 8.950413223

Calculate the square root of the right side: 2.991724122

Break this problem into two subproblems by setting 
(x + -0.3636363637) equal to 2.991724122 and -2.991724122.

Subproblem 1

x + -0.3636363637 = 2.991724122 Simplifying x + -0.3636363637 = 2.991724122 Reorder the terms: -0.3636363637 + x = 2.991724122 Solving -0.3636363637 + x = 2.991724122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = 2.991724122 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = 2.991724122 + 0.3636363637 x = 2.991724122 + 0.3636363637 Combine like terms: 2.991724122 + 0.3636363637 = 3.3553604857 x = 3.3553604857 Simplifying x = 3.3553604857

Subproblem 2

x + -0.3636363637 = -2.991724122 Simplifying x + -0.3636363637 = -2.991724122 Reorder the terms: -0.3636363637 + x = -2.991724122 Solving -0.3636363637 + x = -2.991724122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = -2.991724122 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = -2.991724122 + 0.3636363637 x = -2.991724122 + 0.3636363637 Combine like terms: -2.991724122 + 0.3636363637 = -2.6280877583 x = -2.6280877583 Simplifying x = -2.6280877583

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.3553604857, -2.6280877583}

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