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Simplifying 6x2 + -280x + 2400 = 0 Reorder the terms: 2400 + -280x + 6x2 = 0 Solving 2400 + -280x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1200 + -140x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1200 + -140x + 3x2)' equal to zero and attempt to solve: Simplifying 1200 + -140x + 3x2 = 0 Solving 1200 + -140x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 400 + -46.66666667x + x2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + -46.66666667x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -46.66666667x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -46.66666667x + x2 = 0 + -400 -46.66666667x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -46.66666667x + x2 = -400 The x term is -46.66666667x. Take half its coefficient (-23.33333334). Square it (544.4444448) and add it to both sides. Add '544.4444448' to each side of the equation. -46.66666667x + 544.4444448 + x2 = -400 + 544.4444448 Reorder the terms: 544.4444448 + -46.66666667x + x2 = -400 + 544.4444448 Combine like terms: -400 + 544.4444448 = 144.4444448 544.4444448 + -46.66666667x + x2 = 144.4444448 Factor a perfect square on the left side: (x + -23.33333334)(x + -23.33333334) = 144.4444448 Calculate the square root of the right side: 12.018504266 Break this problem into two subproblems by setting (x + -23.33333334) equal to 12.018504266 and -12.018504266.Subproblem 1
x + -23.33333334 = 12.018504266 Simplifying x + -23.33333334 = 12.018504266 Reorder the terms: -23.33333334 + x = 12.018504266 Solving -23.33333334 + x = 12.018504266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.33333334' to each side of the equation. -23.33333334 + 23.33333334 + x = 12.018504266 + 23.33333334 Combine like terms: -23.33333334 + 23.33333334 = 0.00000000 0.00000000 + x = 12.018504266 + 23.33333334 x = 12.018504266 + 23.33333334 Combine like terms: 12.018504266 + 23.33333334 = 35.351837606 x = 35.351837606 Simplifying x = 35.351837606Subproblem 2
x + -23.33333334 = -12.018504266 Simplifying x + -23.33333334 = -12.018504266 Reorder the terms: -23.33333334 + x = -12.018504266 Solving -23.33333334 + x = -12.018504266 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.33333334' to each side of the equation. -23.33333334 + 23.33333334 + x = -12.018504266 + 23.33333334 Combine like terms: -23.33333334 + 23.33333334 = 0.00000000 0.00000000 + x = -12.018504266 + 23.33333334 x = -12.018504266 + 23.33333334 Combine like terms: -12.018504266 + 23.33333334 = 11.314829074 x = 11.314829074 Simplifying x = 11.314829074Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.351837606, 11.314829074}Solution
x = {35.351837606, 11.314829074}
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