6x^2-4x=17

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Solution for 6x^2-4x=17 equation:


Simplifying
6x2 + -4x = 17

Reorder the terms:
-4x + 6x2 = 17

Solving
-4x + 6x2 = 17

Solving for variable 'x'.

Reorder the terms:
-17 + -4x + 6x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + -4x + 6x2 = 0

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

Divide each side by '6'.
-2.833333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + -0.6666666667x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + -0.6666666667x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 2.833333333
-0.6666666667x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
-0.6666666667x + x2 = 2.833333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 2.833333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 2.833333333 + 0.1111111112

Combine like terms: 2.833333333 + 0.1111111112 = 2.9444444442
0.1111111112 + -0.6666666667x + x2 = 2.9444444442

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 2.9444444442

Calculate the square root of the right side: 1.715938357

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.715938357 and -1.715938357.

Subproblem 1

x + -0.3333333334 = 1.715938357 Simplifying x + -0.3333333334 = 1.715938357 Reorder the terms: -0.3333333334 + x = 1.715938357 Solving -0.3333333334 + x = 1.715938357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 1.715938357 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.715938357 + 0.3333333334 x = 1.715938357 + 0.3333333334 Combine like terms: 1.715938357 + 0.3333333334 = 2.0492716904 x = 2.0492716904 Simplifying x = 2.0492716904

Subproblem 2

x + -0.3333333334 = -1.715938357 Simplifying x + -0.3333333334 = -1.715938357 Reorder the terms: -0.3333333334 + x = -1.715938357 Solving -0.3333333334 + x = -1.715938357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -1.715938357 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.715938357 + 0.3333333334 x = -1.715938357 + 0.3333333334 Combine like terms: -1.715938357 + 0.3333333334 = -1.3826050236 x = -1.3826050236 Simplifying x = -1.3826050236

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.0492716904, -1.3826050236}

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