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Simplifying 0.11x + 0.04x(700 + -1x) = 0.06(700) 0.11x + (700 * 0.04x + -1x * 0.04x) = 0.06(700) 0.11x + (28x + -0.04x2) = 0.06(700) Combine like terms: 0.11x + 28x = 28.11x 28.11x + -0.04x2 = 0.06(700) Multiply 0.06 * 700 28.11x + -0.04x2 = 42 Solving 28.11x + -0.04x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 28.11x + -0.04x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 28.11x + -0.04x2 = 0 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. 1050 + -702.75x + x2 = 0 Move the constant term to the right: Add '-1050' to each side of the equation. 1050 + -702.75x + -1050 + x2 = 0 + -1050 Reorder the terms: 1050 + -1050 + -702.75x + x2 = 0 + -1050 Combine like terms: 1050 + -1050 = 0 0 + -702.75x + x2 = 0 + -1050 -702.75x + x2 = 0 + -1050 Combine like terms: 0 + -1050 = -1050 -702.75x + x2 = -1050 The x term is -702.75x. Take half its coefficient (-351.375). Square it (123464.3906) and add it to both sides. Add '123464.3906' to each side of the equation. -702.75x + 123464.3906 + x2 = -1050 + 123464.3906 Reorder the terms: 123464.3906 + -702.75x + x2 = -1050 + 123464.3906 Combine like terms: -1050 + 123464.3906 = 122414.3906 123464.3906 + -702.75x + x2 = 122414.3906 Factor a perfect square on the left side: (x + -351.375)(x + -351.375) = 122414.3906 Calculate the square root of the right side: 349.877679482 Break this problem into two subproblems by setting (x + -351.375) equal to 349.877679482 and -349.877679482.Subproblem 1
x + -351.375 = 349.877679482 Simplifying x + -351.375 = 349.877679482 Reorder the terms: -351.375 + x = 349.877679482 Solving -351.375 + x = 349.877679482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '351.375' to each side of the equation. -351.375 + 351.375 + x = 349.877679482 + 351.375 Combine like terms: -351.375 + 351.375 = 0.000 0.000 + x = 349.877679482 + 351.375 x = 349.877679482 + 351.375 Combine like terms: 349.877679482 + 351.375 = 701.252679482 x = 701.252679482 Simplifying x = 701.252679482Subproblem 2
x + -351.375 = -349.877679482 Simplifying x + -351.375 = -349.877679482 Reorder the terms: -351.375 + x = -349.877679482 Solving -351.375 + x = -349.877679482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '351.375' to each side of the equation. -351.375 + 351.375 + x = -349.877679482 + 351.375 Combine like terms: -351.375 + 351.375 = 0.000 0.000 + x = -349.877679482 + 351.375 x = -349.877679482 + 351.375 Combine like terms: -349.877679482 + 351.375 = 1.497320518 x = 1.497320518 Simplifying x = 1.497320518Solution
The solution to the problem is based on the solutions from the subproblems. x = {701.252679482, 1.497320518}
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