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Simplifying 6x2 + 100x + -2250 = 0 Reorder the terms: -2250 + 100x + 6x2 = 0 Solving -2250 + 100x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1125 + 50x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1125 + 50x + 3x2)' equal to zero and attempt to solve: Simplifying -1125 + 50x + 3x2 = 0 Solving -1125 + 50x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -375 + 16.66666667x + x2 = 0 Move the constant term to the right: Add '375' to each side of the equation. -375 + 16.66666667x + 375 + x2 = 0 + 375 Reorder the terms: -375 + 375 + 16.66666667x + x2 = 0 + 375 Combine like terms: -375 + 375 = 0 0 + 16.66666667x + x2 = 0 + 375 16.66666667x + x2 = 0 + 375 Combine like terms: 0 + 375 = 375 16.66666667x + x2 = 375 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 = 375 + 69.44444447 Reorder the terms: 69.44444447 + 16.66666667x + x2 = 375 + 69.44444447 Combine like terms: 375 + 69.44444447 = 444.44444447 69.44444447 + 16.66666667x + x2 = 444.44444447 Factor a perfect square on the left side: (x + 8.333333335)(x + 8.333333335) = 444.44444447 Calculate the square root of the right side: 21.081851068 Break this problem into two subproblems by setting (x + 8.333333335) equal to 21.081851068 and -21.081851068.Subproblem 1
x + 8.333333335 = 21.081851068 Simplifying x + 8.333333335 = 21.081851068 Reorder the terms: 8.333333335 + x = 21.081851068 Solving 8.333333335 + x = 21.081851068 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 = 21.081851068 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + x = 21.081851068 + -8.333333335 x = 21.081851068 + -8.333333335 Combine like terms: 21.081851068 + -8.333333335 = 12.748517733 x = 12.748517733 Simplifying x = 12.748517733Subproblem 2
x + 8.333333335 = -21.081851068 Simplifying x + 8.333333335 = -21.081851068 Reorder the terms: 8.333333335 + x = -21.081851068 Solving 8.333333335 + x = -21.081851068 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 = -21.081851068 + -8.333333335 Combine like terms: 8.333333335 + -8.333333335 = 0.000000000 0.000000000 + x = -21.081851068 + -8.333333335 x = -21.081851068 + -8.333333335 Combine like terms: -21.081851068 + -8.333333335 = -29.415184403 x = -29.415184403 Simplifying x = -29.415184403Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.748517733, -29.415184403}Solution
x = {12.748517733, -29.415184403}
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