6x^2-7x+2=33

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Solution for 6x^2-7x+2=33 equation:


Simplifying
6x2 + -7x + 2 = 33

Reorder the terms:
2 + -7x + 6x2 = 33

Solving
2 + -7x + 6x2 = 33

Solving for variable 'x'.

Reorder the terms:
2 + -33 + -7x + 6x2 = 33 + -33

Combine like terms: 2 + -33 = -31
-31 + -7x + 6x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-31 + -7x + 6x2 = 0

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

Divide each side by '6'.
-5.166666667 + -1.166666667x + x2 = 0

Move the constant term to the right:

Add '5.166666667' to each side of the equation.
-5.166666667 + -1.166666667x + 5.166666667 + x2 = 0 + 5.166666667

Reorder the terms:
-5.166666667 + 5.166666667 + -1.166666667x + x2 = 0 + 5.166666667

Combine like terms: -5.166666667 + 5.166666667 = 0.000000000
0.000000000 + -1.166666667x + x2 = 0 + 5.166666667
-1.166666667x + x2 = 0 + 5.166666667

Combine like terms: 0 + 5.166666667 = 5.166666667
-1.166666667x + x2 = 5.166666667

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = 5.166666667 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = 5.166666667 + 0.3402777780

Combine like terms: 5.166666667 + 0.3402777780 = 5.506944445
0.3402777780 + -1.166666667x + x2 = 5.506944445

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 5.506944445

Calculate the square root of the right side: 2.346687974

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 2.346687974 and -2.346687974.

Subproblem 1

x + -0.5833333335 = 2.346687974 Simplifying x + -0.5833333335 = 2.346687974 Reorder the terms: -0.5833333335 + x = 2.346687974 Solving -0.5833333335 + x = 2.346687974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 2.346687974 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 2.346687974 + 0.5833333335 x = 2.346687974 + 0.5833333335 Combine like terms: 2.346687974 + 0.5833333335 = 2.9300213075 x = 2.9300213075 Simplifying x = 2.9300213075

Subproblem 2

x + -0.5833333335 = -2.346687974 Simplifying x + -0.5833333335 = -2.346687974 Reorder the terms: -0.5833333335 + x = -2.346687974 Solving -0.5833333335 + x = -2.346687974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -2.346687974 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -2.346687974 + 0.5833333335 x = -2.346687974 + 0.5833333335 Combine like terms: -2.346687974 + 0.5833333335 = -1.7633546405 x = -1.7633546405 Simplifying x = -1.7633546405

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.9300213075, -1.7633546405}

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