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Simplifying 6x2 + -860x + 12500 = 0 Reorder the terms: 12500 + -860x + 6x2 = 0 Solving 12500 + -860x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6250 + -430x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6250 + -430x + 3x2)' equal to zero and attempt to solve: Simplifying 6250 + -430x + 3x2 = 0 Solving 6250 + -430x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2083.333333 + -143.3333333x + x2 = 0 Move the constant term to the right: Add '-2083.333333' to each side of the equation. 2083.333333 + -143.3333333x + -2083.333333 + x2 = 0 + -2083.333333 Reorder the terms: 2083.333333 + -2083.333333 + -143.3333333x + x2 = 0 + -2083.333333 Combine like terms: 2083.333333 + -2083.333333 = 0.000000 0.000000 + -143.3333333x + x2 = 0 + -2083.333333 -143.3333333x + x2 = 0 + -2083.333333 Combine like terms: 0 + -2083.333333 = -2083.333333 -143.3333333x + x2 = -2083.333333 The x term is -143.3333333x. Take half its coefficient (-71.66666665). Square it (5136.111109) and add it to both sides. Add '5136.111109' to each side of the equation. -143.3333333x + 5136.111109 + x2 = -2083.333333 + 5136.111109 Reorder the terms: 5136.111109 + -143.3333333x + x2 = -2083.333333 + 5136.111109 Combine like terms: -2083.333333 + 5136.111109 = 3052.777776 5136.111109 + -143.3333333x + x2 = 3052.777776 Factor a perfect square on the left side: (x + -71.66666665)(x + -71.66666665) = 3052.777776 Calculate the square root of the right side: 55.251948165 Break this problem into two subproblems by setting (x + -71.66666665) equal to 55.251948165 and -55.251948165.Subproblem 1
x + -71.66666665 = 55.251948165 Simplifying x + -71.66666665 = 55.251948165 Reorder the terms: -71.66666665 + x = 55.251948165 Solving -71.66666665 + x = 55.251948165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.66666665' to each side of the equation. -71.66666665 + 71.66666665 + x = 55.251948165 + 71.66666665 Combine like terms: -71.66666665 + 71.66666665 = 0.00000000 0.00000000 + x = 55.251948165 + 71.66666665 x = 55.251948165 + 71.66666665 Combine like terms: 55.251948165 + 71.66666665 = 126.918614815 x = 126.918614815 Simplifying x = 126.918614815Subproblem 2
x + -71.66666665 = -55.251948165 Simplifying x + -71.66666665 = -55.251948165 Reorder the terms: -71.66666665 + x = -55.251948165 Solving -71.66666665 + x = -55.251948165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.66666665' to each side of the equation. -71.66666665 + 71.66666665 + x = -55.251948165 + 71.66666665 Combine like terms: -71.66666665 + 71.66666665 = 0.00000000 0.00000000 + x = -55.251948165 + 71.66666665 x = -55.251948165 + 71.66666665 Combine like terms: -55.251948165 + 71.66666665 = 16.414718485 x = 16.414718485 Simplifying x = 16.414718485Solution
The solution to the problem is based on the solutions from the subproblems. x = {126.918614815, 16.414718485}Solution
x = {126.918614815, 16.414718485}
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