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Simplifying 0.11x + 0.08x(165000 + -1x) = 15750 0.11x + (165000 * 0.08x + -1x * 0.08x) = 15750 0.11x + (13200x + -0.08x2) = 15750 Combine like terms: 0.11x + 13200x = 13200.11x 13200.11x + -0.08x2 = 15750 Solving 13200.11x + -0.08x2 = 15750 Solving for variable 'x'. Reorder the terms: -15750 + 13200.11x + -0.08x2 = 15750 + -15750 Combine like terms: 15750 + -15750 = 0 -15750 + 13200.11x + -0.08x2 = 0 Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. 196875 + -165001.375x + x2 = 0 Move the constant term to the right: Add '-196875' to each side of the equation. 196875 + -165001.375x + -196875 + x2 = 0 + -196875 Reorder the terms: 196875 + -196875 + -165001.375x + x2 = 0 + -196875 Combine like terms: 196875 + -196875 = 0 0 + -165001.375x + x2 = 0 + -196875 -165001.375x + x2 = 0 + -196875 Combine like terms: 0 + -196875 = -196875 -165001.375x + x2 = -196875 The x term is -165001.375x. Take half its coefficient (-82500.6875). Square it (6806363438) and add it to both sides. Add '6806363438' to each side of the equation. -165001.375x + 6806363438 + x2 = -196875 + 6806363438 Reorder the terms: 6806363438 + -165001.375x + x2 = -196875 + 6806363438 Combine like terms: -196875 + 6806363438 = 6806166563 6806363438 + -165001.375x + x2 = 6806166563 Factor a perfect square on the left side: (x + -82500.6875)(x + -82500.6875) = 6806166563 Calculate the square root of the right side: 82499.494319662 Break this problem into two subproblems by setting (x + -82500.6875) equal to 82499.494319662 and -82499.494319662.Subproblem 1
x + -82500.6875 = 82499.494319662 Simplifying x + -82500.6875 = 82499.494319662 Reorder the terms: -82500.6875 + x = 82499.494319662 Solving -82500.6875 + x = 82499.494319662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '82500.6875' to each side of the equation. -82500.6875 + 82500.6875 + x = 82499.494319662 + 82500.6875 Combine like terms: -82500.6875 + 82500.6875 = 0.0000 0.0000 + x = 82499.494319662 + 82500.6875 x = 82499.494319662 + 82500.6875 Combine like terms: 82499.494319662 + 82500.6875 = 165000.181819662 x = 165000.181819662 Simplifying x = 165000.181819662Subproblem 2
x + -82500.6875 = -82499.494319662 Simplifying x + -82500.6875 = -82499.494319662 Reorder the terms: -82500.6875 + x = -82499.494319662 Solving -82500.6875 + x = -82499.494319662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '82500.6875' to each side of the equation. -82500.6875 + 82500.6875 + x = -82499.494319662 + 82500.6875 Combine like terms: -82500.6875 + 82500.6875 = 0.0000 0.0000 + x = -82499.494319662 + 82500.6875 x = -82499.494319662 + 82500.6875 Combine like terms: -82499.494319662 + 82500.6875 = 1.193180338 x = 1.193180338 Simplifying x = 1.193180338Solution
The solution to the problem is based on the solutions from the subproblems. x = {165000.181819662, 1.193180338}
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