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Simplifying 300000 = (10000 + 10000(x + -1) * 6000) * x Reorder the terms: 300000 = (10000 + 10000(-1 + x) * 6000) * x Reorder the terms for easier multiplication: 300000 = (10000 + 10000 * 6000(-1 + x)) * x Multiply 10000 * 6000 300000 = (10000 + 60000000(-1 + x)) * x 300000 = (10000 + (-1 * 60000000 + x * 60000000)) * x 300000 = (10000 + (-60000000 + 60000000x)) * x Combine like terms: 10000 + -60000000 = -59990000 300000 = (-59990000 + 60000000x) * x Reorder the terms for easier multiplication: 300000 = x(-59990000 + 60000000x) 300000 = (-59990000 * x + 60000000x * x) 300000 = (-59990000x + 60000000x2) Solving 300000 = -59990000x + 60000000x2 Solving for variable 'x'. Reorder the terms: 300000 + 59990000x + -60000000x2 = -59990000x + 59990000x + 60000000x2 + -60000000x2 Combine like terms: -59990000x + 59990000x = 0 300000 + 59990000x + -60000000x2 = 0 + 60000000x2 + -60000000x2 300000 + 59990000x + -60000000x2 = 60000000x2 + -60000000x2 Combine like terms: 60000000x2 + -60000000x2 = 0 300000 + 59990000x + -60000000x2 = 0 Factor out the Greatest Common Factor (GCF), '10000'. 10000(30 + 5999x + -6000x2) = 0 Ignore the factor 10000.Subproblem 1
Set the factor '(30 + 5999x + -6000x2)' equal to zero and attempt to solve: Simplifying 30 + 5999x + -6000x2 = 0 Solving 30 + 5999x + -6000x2 = 0 Begin completing the square. Divide all terms by -6000 the coefficient of the squared term: Divide each side by '-6000'. -0.005 + -0.9998333333x + x2 = 0.000 Move the constant term to the right: Add '0.005' to each side of the equation. -0.005 + -0.9998333333x + 0.005 + x2 = 0.000 + 0.005 Reorder the terms: -0.005 + 0.005 + -0.9998333333x + x2 = 0.000 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + -0.9998333333x + x2 = 0.000 + 0.005 -0.9998333333x + x2 = 0.000 + 0.005 Combine like terms: 0.000 + 0.005 = 0.005 -0.9998333333x + x2 = 0.005 The x term is -0.9998333333x. Take half its coefficient (-0.4999166667). Square it (0.2499166736) and add it to both sides. Add '0.2499166736' to each side of the equation. -0.9998333333x + 0.2499166736 + x2 = 0.005 + 0.2499166736 Reorder the terms: 0.2499166736 + -0.9998333333x + x2 = 0.005 + 0.2499166736 Combine like terms: 0.005 + 0.2499166736 = 0.2549166736 0.2499166736 + -0.9998333333x + x2 = 0.2549166736 Factor a perfect square on the left side: (x + -0.4999166667)(x + -0.4999166667) = 0.2549166736 Calculate the square root of the right side: 0.504892735 Break this problem into two subproblems by setting (x + -0.4999166667) equal to 0.504892735 and -0.504892735.Subproblem 1
x + -0.4999166667 = 0.504892735 Simplifying x + -0.4999166667 = 0.504892735 Reorder the terms: -0.4999166667 + x = 0.504892735 Solving -0.4999166667 + x = 0.504892735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4999166667' to each side of the equation. -0.4999166667 + 0.4999166667 + x = 0.504892735 + 0.4999166667 Combine like terms: -0.4999166667 + 0.4999166667 = 0.0000000000 0.0000000000 + x = 0.504892735 + 0.4999166667 x = 0.504892735 + 0.4999166667 Combine like terms: 0.504892735 + 0.4999166667 = 1.0048094017 x = 1.0048094017 Simplifying x = 1.0048094017Subproblem 2
x + -0.4999166667 = -0.504892735 Simplifying x + -0.4999166667 = -0.504892735 Reorder the terms: -0.4999166667 + x = -0.504892735 Solving -0.4999166667 + x = -0.504892735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4999166667' to each side of the equation. -0.4999166667 + 0.4999166667 + x = -0.504892735 + 0.4999166667 Combine like terms: -0.4999166667 + 0.4999166667 = 0.0000000000 0.0000000000 + x = -0.504892735 + 0.4999166667 x = -0.504892735 + 0.4999166667 Combine like terms: -0.504892735 + 0.4999166667 = -0.0049760683 x = -0.0049760683 Simplifying x = -0.0049760683Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0048094017, -0.0049760683}Solution
x = {1.0048094017, -0.0049760683}
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