2x^2-3x=66

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Solution for 2x^2-3x=66 equation:


Simplifying
2x2 + -3x = 66

Reorder the terms:
-3x + 2x2 = 66

Solving
-3x + 2x2 = 66

Solving for variable 'x'.

Reorder the terms:
-66 + -3x + 2x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + -3x + 2x2 = 0

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

Divide each side by '2'.
-33 + -1.5x + x2 = 0

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -1.5x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -1.5x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -1.5x + x2 = 0 + 33
-1.5x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-1.5x + x2 = 33

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 33 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 33 + 0.5625

Combine like terms: 33 + 0.5625 = 33.5625
0.5625 + -1.5x + x2 = 33.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 33.5625

Calculate the square root of the right side: 5.793315113

Break this problem into two subproblems by setting 
(x + -0.75) equal to 5.793315113 and -5.793315113.

Subproblem 1

x + -0.75 = 5.793315113 Simplifying x + -0.75 = 5.793315113 Reorder the terms: -0.75 + x = 5.793315113 Solving -0.75 + x = 5.793315113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 5.793315113 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 5.793315113 + 0.75 x = 5.793315113 + 0.75 Combine like terms: 5.793315113 + 0.75 = 6.543315113 x = 6.543315113 Simplifying x = 6.543315113

Subproblem 2

x + -0.75 = -5.793315113 Simplifying x + -0.75 = -5.793315113 Reorder the terms: -0.75 + x = -5.793315113 Solving -0.75 + x = -5.793315113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -5.793315113 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -5.793315113 + 0.75 x = -5.793315113 + 0.75 Combine like terms: -5.793315113 + 0.75 = -5.043315113 x = -5.043315113 Simplifying x = -5.043315113

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.543315113, -5.043315113}

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