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Simplifying -15050 + 2000x + -48x2 = 0 Solving -15050 + 2000x + -48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7525 + 1000x + -24x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7525 + 1000x + -24x2)' equal to zero and attempt to solve: Simplifying -7525 + 1000x + -24x2 = 0 Solving -7525 + 1000x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. 313.5416667 + -41.66666667x + x2 = 0 Move the constant term to the right: Add '-313.5416667' to each side of the equation. 313.5416667 + -41.66666667x + -313.5416667 + x2 = 0 + -313.5416667 Reorder the terms: 313.5416667 + -313.5416667 + -41.66666667x + x2 = 0 + -313.5416667 Combine like terms: 313.5416667 + -313.5416667 = 0.0000000 0.0000000 + -41.66666667x + x2 = 0 + -313.5416667 -41.66666667x + x2 = 0 + -313.5416667 Combine like terms: 0 + -313.5416667 = -313.5416667 -41.66666667x + x2 = -313.5416667 The x term is -41.66666667x. Take half its coefficient (-20.83333334). Square it (434.0277781) and add it to both sides. Add '434.0277781' to each side of the equation. -41.66666667x + 434.0277781 + x2 = -313.5416667 + 434.0277781 Reorder the terms: 434.0277781 + -41.66666667x + x2 = -313.5416667 + 434.0277781 Combine like terms: -313.5416667 + 434.0277781 = 120.4861114 434.0277781 + -41.66666667x + x2 = 120.4861114 Factor a perfect square on the left side: (x + -20.83333334)(x + -20.83333334) = 120.4861114 Calculate the square root of the right side: 10.976616573 Break this problem into two subproblems by setting (x + -20.83333334) equal to 10.976616573 and -10.976616573.Subproblem 1
x + -20.83333334 = 10.976616573 Simplifying x + -20.83333334 = 10.976616573 Reorder the terms: -20.83333334 + x = 10.976616573 Solving -20.83333334 + x = 10.976616573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.83333334' to each side of the equation. -20.83333334 + 20.83333334 + x = 10.976616573 + 20.83333334 Combine like terms: -20.83333334 + 20.83333334 = 0.00000000 0.00000000 + x = 10.976616573 + 20.83333334 x = 10.976616573 + 20.83333334 Combine like terms: 10.976616573 + 20.83333334 = 31.809949913 x = 31.809949913 Simplifying x = 31.809949913Subproblem 2
x + -20.83333334 = -10.976616573 Simplifying x + -20.83333334 = -10.976616573 Reorder the terms: -20.83333334 + x = -10.976616573 Solving -20.83333334 + x = -10.976616573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.83333334' to each side of the equation. -20.83333334 + 20.83333334 + x = -10.976616573 + 20.83333334 Combine like terms: -20.83333334 + 20.83333334 = 0.00000000 0.00000000 + x = -10.976616573 + 20.83333334 x = -10.976616573 + 20.83333334 Combine like terms: -10.976616573 + 20.83333334 = 9.856716767 x = 9.856716767 Simplifying x = 9.856716767Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.809949913, 9.856716767}Solution
x = {31.809949913, 9.856716767}
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