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Simplifying 0.06x(12000 + -1x)(0.02) = 12000 Reorder the terms for easier multiplication: 0.06 * 0.02x(12000 + -1x) = 12000 Multiply 0.06 * 0.02 0.0012x(12000 + -1x) = 12000 (12000 * 0.0012x + -1x * 0.0012x) = 12000 (14.4x + -0.0012x2) = 12000 Solving 14.4x + -0.0012x2 = 12000 Solving for variable 'x'. Reorder the terms: -12000 + 14.4x + -0.0012x2 = 12000 + -12000 Combine like terms: 12000 + -12000 = 0 -12000 + 14.4x + -0.0012x2 = 0 Begin completing the square. Divide all terms by -0.0012 the coefficient of the squared term: Divide each side by '-0.0012'. 10000000 + -12000x + x2 = 0 Move the constant term to the right: Add '-10000000' to each side of the equation. 10000000 + -12000x + -10000000 + x2 = 0 + -10000000 Reorder the terms: 10000000 + -10000000 + -12000x + x2 = 0 + -10000000 Combine like terms: 10000000 + -10000000 = 0 0 + -12000x + x2 = 0 + -10000000 -12000x + x2 = 0 + -10000000 Combine like terms: 0 + -10000000 = -10000000 -12000x + x2 = -10000000 The x term is -12000x. Take half its coefficient (-6000). Square it (36000000) and add it to both sides. Add '36000000' to each side of the equation. -12000x + 36000000 + x2 = -10000000 + 36000000 Reorder the terms: 36000000 + -12000x + x2 = -10000000 + 36000000 Combine like terms: -10000000 + 36000000 = 26000000 36000000 + -12000x + x2 = 26000000 Factor a perfect square on the left side: (x + -6000)(x + -6000) = 26000000 Calculate the square root of the right side: 5099.019513593 Break this problem into two subproblems by setting (x + -6000) equal to 5099.019513593 and -5099.019513593.Subproblem 1
x + -6000 = 5099.019513593 Simplifying x + -6000 = 5099.019513593 Reorder the terms: -6000 + x = 5099.019513593 Solving -6000 + x = 5099.019513593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6000' to each side of the equation. -6000 + 6000 + x = 5099.019513593 + 6000 Combine like terms: -6000 + 6000 = 0 0 + x = 5099.019513593 + 6000 x = 5099.019513593 + 6000 Combine like terms: 5099.019513593 + 6000 = 11099.019513593 x = 11099.019513593 Simplifying x = 11099.019513593Subproblem 2
x + -6000 = -5099.019513593 Simplifying x + -6000 = -5099.019513593 Reorder the terms: -6000 + x = -5099.019513593 Solving -6000 + x = -5099.019513593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6000' to each side of the equation. -6000 + 6000 + x = -5099.019513593 + 6000 Combine like terms: -6000 + 6000 = 0 0 + x = -5099.019513593 + 6000 x = -5099.019513593 + 6000 Combine like terms: -5099.019513593 + 6000 = 900.980486407 x = 900.980486407 Simplifying x = 900.980486407Solution
The solution to the problem is based on the solutions from the subproblems. x = {11099.019513593, 900.980486407}
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