11x^2-17=4x

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Solution for 11x^2-17=4x equation:


Simplifying
11x2 + -17 = 4x

Reorder the terms:
-17 + 11x2 = 4x

Solving
-17 + 11x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-17 + -4x + 11x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-17 + -4x + 11x2 = 0

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

Divide each side by '11'.
-1.545454545 + -0.3636363636x + x2 = 0

Move the constant term to the right:

Add '1.545454545' to each side of the equation.
-1.545454545 + -0.3636363636x + 1.545454545 + x2 = 0 + 1.545454545

Reorder the terms:
-1.545454545 + 1.545454545 + -0.3636363636x + x2 = 0 + 1.545454545

Combine like terms: -1.545454545 + 1.545454545 = 0.000000000
0.000000000 + -0.3636363636x + x2 = 0 + 1.545454545
-0.3636363636x + x2 = 0 + 1.545454545

Combine like terms: 0 + 1.545454545 = 1.545454545
-0.3636363636x + x2 = 1.545454545

The x term is -0.3636363636x.  Take half its coefficient (-0.1818181818).
Square it (0.03305785123) and add it to both sides.

Add '0.03305785123' to each side of the equation.
-0.3636363636x + 0.03305785123 + x2 = 1.545454545 + 0.03305785123

Reorder the terms:
0.03305785123 + -0.3636363636x + x2 = 1.545454545 + 0.03305785123

Combine like terms: 1.545454545 + 0.03305785123 = 1.57851239623
0.03305785123 + -0.3636363636x + x2 = 1.57851239623

Factor a perfect square on the left side:
(x + -0.1818181818)(x + -0.1818181818) = 1.57851239623

Calculate the square root of the right side: 1.256388633

Break this problem into two subproblems by setting 
(x + -0.1818181818) equal to 1.256388633 and -1.256388633.

Subproblem 1

x + -0.1818181818 = 1.256388633 Simplifying x + -0.1818181818 = 1.256388633 Reorder the terms: -0.1818181818 + x = 1.256388633 Solving -0.1818181818 + x = 1.256388633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = 1.256388633 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 1.256388633 + 0.1818181818 x = 1.256388633 + 0.1818181818 Combine like terms: 1.256388633 + 0.1818181818 = 1.4382068148 x = 1.4382068148 Simplifying x = 1.4382068148

Subproblem 2

x + -0.1818181818 = -1.256388633 Simplifying x + -0.1818181818 = -1.256388633 Reorder the terms: -0.1818181818 + x = -1.256388633 Solving -0.1818181818 + x = -1.256388633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = -1.256388633 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -1.256388633 + 0.1818181818 x = -1.256388633 + 0.1818181818 Combine like terms: -1.256388633 + 0.1818181818 = -1.0745704512 x = -1.0745704512 Simplifying x = -1.0745704512

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4382068148, -1.0745704512}

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