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Simplifying 36x2 + -60x = 33 Reorder the terms: -60x + 36x2 = 33 Solving -60x + 36x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + -60x + 36x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -60x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + -20x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + -20x + 12x2)' equal to zero and attempt to solve: Simplifying -11 + -20x + 12x2 = 0 Solving -11 + -20x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.9166666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + -1.666666667x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + -1.666666667x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + -1.666666667x + x2 = 0 + 0.9166666667 -1.666666667x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 -1.666666667x + x2 = 0.9166666667 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 = 0.9166666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 0.9166666667 + 0.6944444447 Combine like terms: 0.9166666667 + 0.6944444447 = 1.6111111114 0.6944444447 + -1.666666667x + x2 = 1.6111111114 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 1.6111111114 Calculate the square root of the right side: 1.269295518 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.269295518 and -1.269295518.Subproblem 1
x + -0.8333333335 = 1.269295518 Simplifying x + -0.8333333335 = 1.269295518 Reorder the terms: -0.8333333335 + x = 1.269295518 Solving -0.8333333335 + x = 1.269295518 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 = 1.269295518 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.269295518 + 0.8333333335 x = 1.269295518 + 0.8333333335 Combine like terms: 1.269295518 + 0.8333333335 = 2.1026288515 x = 2.1026288515 Simplifying x = 2.1026288515Subproblem 2
x + -0.8333333335 = -1.269295518 Simplifying x + -0.8333333335 = -1.269295518 Reorder the terms: -0.8333333335 + x = -1.269295518 Solving -0.8333333335 + x = -1.269295518 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 = -1.269295518 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.269295518 + 0.8333333335 x = -1.269295518 + 0.8333333335 Combine like terms: -1.269295518 + 0.8333333335 = -0.4359621845 x = -0.4359621845 Simplifying x = -0.4359621845Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1026288515, -0.4359621845}Solution
x = {2.1026288515, -0.4359621845}
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