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Simplifying 150 = -6x2 + 100x + -180 Reorder the terms: 150 = -180 + 100x + -6x2 Solving 150 = -180 + 100x + -6x2 Solving for variable 'x'. Combine like terms: 150 + 180 = 330 330 + -100x + 6x2 = -180 + 100x + -6x2 + 180 + -100x + 6x2 Reorder the terms: 330 + -100x + 6x2 = -180 + 180 + 100x + -100x + -6x2 + 6x2 Combine like terms: -180 + 180 = 0 330 + -100x + 6x2 = 0 + 100x + -100x + -6x2 + 6x2 330 + -100x + 6x2 = 100x + -100x + -6x2 + 6x2 Combine like terms: 100x + -100x = 0 330 + -100x + 6x2 = 0 + -6x2 + 6x2 330 + -100x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 330 + -100x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(165 + -50x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(165 + -50x + 3x2)' equal to zero and attempt to solve: Simplifying 165 + -50x + 3x2 = 0 Solving 165 + -50x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 55 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '-55' to each side of the equation. 55 + -16.66666667x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + -16.66666667x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -16.66666667x + x2 = 0 + -55 -16.66666667x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 -16.66666667x + x2 = -55 The x term is -16.66666667x. Take half its coefficient (-8.333333335). Square it (69.44444447) and add it to both sides. Add '69.44444447' to each side of the equation. -16.66666667x + 69.44444447 + x2 = -55 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = -55 + 69.44444447 Combine like terms: -55 + 69.44444447 = 14.44444447 69.44444447 + -16.66666667x + x2 = 14.44444447 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 14.44444447 Calculate the square root of the right side: 3.800584754 Break this problem into two subproblems by setting (x + -8.333333335) equal to 3.800584754 and -3.800584754.Subproblem 1
x + -8.333333335 = 3.800584754 Simplifying x + -8.333333335 = 3.800584754 Reorder the terms: -8.333333335 + x = 3.800584754 Solving -8.333333335 + x = 3.800584754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = 3.800584754 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 3.800584754 + 8.333333335 x = 3.800584754 + 8.333333335 Combine like terms: 3.800584754 + 8.333333335 = 12.133918089 x = 12.133918089 Simplifying x = 12.133918089Subproblem 2
x + -8.333333335 = -3.800584754 Simplifying x + -8.333333335 = -3.800584754 Reorder the terms: -8.333333335 + x = -3.800584754 Solving -8.333333335 + x = -3.800584754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = -3.800584754 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -3.800584754 + 8.333333335 x = -3.800584754 + 8.333333335 Combine like terms: -3.800584754 + 8.333333335 = 4.532748581 x = 4.532748581 Simplifying x = 4.532748581Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.133918089, 4.532748581}Solution
x = {12.133918089, 4.532748581}
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