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Simplifying 26x2 + 370x + -23700 = 0 Reorder the terms: -23700 + 370x + 26x2 = 0 Solving -23700 + 370x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11850 + 185x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11850 + 185x + 13x2)' equal to zero and attempt to solve: Simplifying -11850 + 185x + 13x2 = 0 Solving -11850 + 185x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -911.5384615 + 14.23076923x + x2 = 0 Move the constant term to the right: Add '911.5384615' to each side of the equation. -911.5384615 + 14.23076923x + 911.5384615 + x2 = 0 + 911.5384615 Reorder the terms: -911.5384615 + 911.5384615 + 14.23076923x + x2 = 0 + 911.5384615 Combine like terms: -911.5384615 + 911.5384615 = 0.0000000 0.0000000 + 14.23076923x + x2 = 0 + 911.5384615 14.23076923x + x2 = 0 + 911.5384615 Combine like terms: 0 + 911.5384615 = 911.5384615 14.23076923x + x2 = 911.5384615 The x term is 14.23076923x. Take half its coefficient (7.115384615). Square it (50.62869822) and add it to both sides. Add '50.62869822' to each side of the equation. 14.23076923x + 50.62869822 + x2 = 911.5384615 + 50.62869822 Reorder the terms: 50.62869822 + 14.23076923x + x2 = 911.5384615 + 50.62869822 Combine like terms: 911.5384615 + 50.62869822 = 962.16715972 50.62869822 + 14.23076923x + x2 = 962.16715972 Factor a perfect square on the left side: (x + 7.115384615)(x + 7.115384615) = 962.16715972 Calculate the square root of the right side: 31.018819444 Break this problem into two subproblems by setting (x + 7.115384615) equal to 31.018819444 and -31.018819444.Subproblem 1
x + 7.115384615 = 31.018819444 Simplifying x + 7.115384615 = 31.018819444 Reorder the terms: 7.115384615 + x = 31.018819444 Solving 7.115384615 + x = 31.018819444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.115384615' to each side of the equation. 7.115384615 + -7.115384615 + x = 31.018819444 + -7.115384615 Combine like terms: 7.115384615 + -7.115384615 = 0.000000000 0.000000000 + x = 31.018819444 + -7.115384615 x = 31.018819444 + -7.115384615 Combine like terms: 31.018819444 + -7.115384615 = 23.903434829 x = 23.903434829 Simplifying x = 23.903434829Subproblem 2
x + 7.115384615 = -31.018819444 Simplifying x + 7.115384615 = -31.018819444 Reorder the terms: 7.115384615 + x = -31.018819444 Solving 7.115384615 + x = -31.018819444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.115384615' to each side of the equation. 7.115384615 + -7.115384615 + x = -31.018819444 + -7.115384615 Combine like terms: 7.115384615 + -7.115384615 = 0.000000000 0.000000000 + x = -31.018819444 + -7.115384615 x = -31.018819444 + -7.115384615 Combine like terms: -31.018819444 + -7.115384615 = -38.134204059 x = -38.134204059 Simplifying x = -38.134204059Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.903434829, -38.134204059}Solution
x = {23.903434829, -38.134204059}
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