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Simplifying 0.04x + 0.07x(15000 + -1x) = 900 0.04x + (15000 * 0.07x + -1x * 0.07x) = 900 0.04x + (1050x + -0.07x2) = 900 Combine like terms: 0.04x + 1050x = 1050.04x 1050.04x + -0.07x2 = 900 Solving 1050.04x + -0.07x2 = 900 Solving for variable 'x'. Reorder the terms: -900 + 1050.04x + -0.07x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -900 + 1050.04x + -0.07x2 = 0 Begin completing the square. Divide all terms by -0.07 the coefficient of the squared term: Divide each side by '-0.07'. 12857.14286 + -15000.57143x + x2 = 0 Move the constant term to the right: Add '-12857.14286' to each side of the equation. 12857.14286 + -15000.57143x + -12857.14286 + x2 = 0 + -12857.14286 Reorder the terms: 12857.14286 + -12857.14286 + -15000.57143x + x2 = 0 + -12857.14286 Combine like terms: 12857.14286 + -12857.14286 = 0.00000 0.00000 + -15000.57143x + x2 = 0 + -12857.14286 -15000.57143x + x2 = 0 + -12857.14286 Combine like terms: 0 + -12857.14286 = -12857.14286 -15000.57143x + x2 = -12857.14286 The x term is -15000.57143x. Take half its coefficient (-7500.285715). Square it (56254285.81) and add it to both sides. Add '56254285.81' to each side of the equation. -15000.57143x + 56254285.81 + x2 = -12857.14286 + 56254285.81 Reorder the terms: 56254285.81 + -15000.57143x + x2 = -12857.14286 + 56254285.81 Combine like terms: -12857.14286 + 56254285.81 = 56241428.66714 56254285.81 + -15000.57143x + x2 = 56241428.66714 Factor a perfect square on the left side: (x + -7500.285715)(x + -7500.285715) = 56241428.66714 Calculate the square root of the right side: 7499.428556039 Break this problem into two subproblems by setting (x + -7500.285715) equal to 7499.428556039 and -7499.428556039.Subproblem 1
x + -7500.285715 = 7499.428556039 Simplifying x + -7500.285715 = 7499.428556039 Reorder the terms: -7500.285715 + x = 7499.428556039 Solving -7500.285715 + x = 7499.428556039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7500.285715' to each side of the equation. -7500.285715 + 7500.285715 + x = 7499.428556039 + 7500.285715 Combine like terms: -7500.285715 + 7500.285715 = 0.000000 0.000000 + x = 7499.428556039 + 7500.285715 x = 7499.428556039 + 7500.285715 Combine like terms: 7499.428556039 + 7500.285715 = 14999.714271039 x = 14999.714271039 Simplifying x = 14999.714271039Subproblem 2
x + -7500.285715 = -7499.428556039 Simplifying x + -7500.285715 = -7499.428556039 Reorder the terms: -7500.285715 + x = -7499.428556039 Solving -7500.285715 + x = -7499.428556039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7500.285715' to each side of the equation. -7500.285715 + 7500.285715 + x = -7499.428556039 + 7500.285715 Combine like terms: -7500.285715 + 7500.285715 = 0.000000 0.000000 + x = -7499.428556039 + 7500.285715 x = -7499.428556039 + 7500.285715 Combine like terms: -7499.428556039 + 7500.285715 = 0.857158961 x = 0.857158961 Simplifying x = 0.857158961Solution
The solution to the problem is based on the solutions from the subproblems. x = {14999.714271039, 0.857158961}
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