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Simplifying 2235.87 = 85.9x + x2 Solving 2235.87 = 85.9x + x2 Solving for variable 'x'. Reorder the terms: 2235.87 + -85.9x + -1x2 = 85.9x + -85.9x + x2 + -1x2 Combine like terms: 85.9x + -85.9x = 0.0 2235.87 + -85.9x + -1x2 = 0.0 + x2 + -1x2 2235.87 + -85.9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2235.87 + -85.9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2235.87 + 85.9x + x2 = 0 Move the constant term to the right: Add '2235.87' to each side of the equation. -2235.87 + 85.9x + 2235.87 + x2 = 0 + 2235.87 Reorder the terms: -2235.87 + 2235.87 + 85.9x + x2 = 0 + 2235.87 Combine like terms: -2235.87 + 2235.87 = 0.00 0.00 + 85.9x + x2 = 0 + 2235.87 85.9x + x2 = 0 + 2235.87 Combine like terms: 0 + 2235.87 = 2235.87 85.9x + x2 = 2235.87 The x term is 85.9x. Take half its coefficient (42.95). Square it (1844.7025) and add it to both sides. Add '1844.7025' to each side of the equation. 85.9x + 1844.7025 + x2 = 2235.87 + 1844.7025 Reorder the terms: 1844.7025 + 85.9x + x2 = 2235.87 + 1844.7025 Combine like terms: 2235.87 + 1844.7025 = 4080.5725 1844.7025 + 85.9x + x2 = 4080.5725 Factor a perfect square on the left side: (x + 42.95)(x + 42.95) = 4080.5725 Calculate the square root of the right side: 63.879358951 Break this problem into two subproblems by setting (x + 42.95) equal to 63.879358951 and -63.879358951.Subproblem 1
x + 42.95 = 63.879358951 Simplifying x + 42.95 = 63.879358951 Reorder the terms: 42.95 + x = 63.879358951 Solving 42.95 + x = 63.879358951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.95' to each side of the equation. 42.95 + -42.95 + x = 63.879358951 + -42.95 Combine like terms: 42.95 + -42.95 = 0.00 0.00 + x = 63.879358951 + -42.95 x = 63.879358951 + -42.95 Combine like terms: 63.879358951 + -42.95 = 20.929358951 x = 20.929358951 Simplifying x = 20.929358951Subproblem 2
x + 42.95 = -63.879358951 Simplifying x + 42.95 = -63.879358951 Reorder the terms: 42.95 + x = -63.879358951 Solving 42.95 + x = -63.879358951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.95' to each side of the equation. 42.95 + -42.95 + x = -63.879358951 + -42.95 Combine like terms: 42.95 + -42.95 = 0.00 0.00 + x = -63.879358951 + -42.95 x = -63.879358951 + -42.95 Combine like terms: -63.879358951 + -42.95 = -106.829358951 x = -106.829358951 Simplifying x = -106.829358951Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.929358951, -106.829358951}
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