6x^2-10x+6=59

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Solution for 6x^2-10x+6=59 equation:


Simplifying
6x2 + -10x + 6 = 59

Reorder the terms:
6 + -10x + 6x2 = 59

Solving
6 + -10x + 6x2 = 59

Solving for variable 'x'.

Reorder the terms:
6 + -59 + -10x + 6x2 = 59 + -59

Combine like terms: 6 + -59 = -53
-53 + -10x + 6x2 = 59 + -59

Combine like terms: 59 + -59 = 0
-53 + -10x + 6x2 = 0

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

Divide each side by '6'.
-8.833333333 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '8.833333333' to each side of the equation.
-8.833333333 + -1.666666667x + 8.833333333 + x2 = 0 + 8.833333333

Reorder the terms:
-8.833333333 + 8.833333333 + -1.666666667x + x2 = 0 + 8.833333333

Combine like terms: -8.833333333 + 8.833333333 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + 8.833333333
-1.666666667x + x2 = 0 + 8.833333333

Combine like terms: 0 + 8.833333333 = 8.833333333
-1.666666667x + x2 = 8.833333333

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 8.833333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 8.833333333 + 0.6944444447

Combine like terms: 8.833333333 + 0.6944444447 = 9.5277777777
0.6944444447 + -1.666666667x + x2 = 9.5277777777

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 9.5277777777

Calculate the square root of the right side: 3.086709863

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 3.086709863 and -3.086709863.

Subproblem 1

x + -0.8333333335 = 3.086709863 Simplifying x + -0.8333333335 = 3.086709863 Reorder the terms: -0.8333333335 + x = 3.086709863 Solving -0.8333333335 + x = 3.086709863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 3.086709863 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 3.086709863 + 0.8333333335 x = 3.086709863 + 0.8333333335 Combine like terms: 3.086709863 + 0.8333333335 = 3.9200431965 x = 3.9200431965 Simplifying x = 3.9200431965

Subproblem 2

x + -0.8333333335 = -3.086709863 Simplifying x + -0.8333333335 = -3.086709863 Reorder the terms: -0.8333333335 + x = -3.086709863 Solving -0.8333333335 + x = -3.086709863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -3.086709863 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -3.086709863 + 0.8333333335 x = -3.086709863 + 0.8333333335 Combine like terms: -3.086709863 + 0.8333333335 = -2.2533765295 x = -2.2533765295 Simplifying x = -2.2533765295

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.9200431965, -2.2533765295}

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