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Simplifying -0.33x2 + 95.2x + 5846.07 = 91.31000000 Reorder the terms: 5846.07 + 95.2x + -0.33x2 = 91.31000000 Solving 5846.07 + 95.2x + -0.33x2 = 91.31000000 Solving for variable 'x'. Reorder the terms: 5846.07 + -91.31000000 + 95.2x + -0.33x2 = 91.31000000 + -91.31000000 Combine like terms: 5846.07 + -91.31000000 = 5754.76 5754.76 + 95.2x + -0.33x2 = 91.31000000 + -91.31000000 Combine like terms: 91.31000000 + -91.31000000 = 0.00000000 5754.76 + 95.2x + -0.33x2 = 0.00000000 Begin completing the square. Divide all terms by -0.33 the coefficient of the squared term: Divide each side by '-0.33'. -17438.66667 + -288.4848485x + x2 = 0.000000 Move the constant term to the right: Add '17438.66667' to each side of the equation. -17438.66667 + -288.4848485x + 17438.66667 + x2 = 0.000000 + 17438.66667 Reorder the terms: -17438.66667 + 17438.66667 + -288.4848485x + x2 = 0.000000 + 17438.66667 Combine like terms: -17438.66667 + 17438.66667 = 0.00000 0.00000 + -288.4848485x + x2 = 0.000000 + 17438.66667 -288.4848485x + x2 = 0.000000 + 17438.66667 Combine like terms: 0.000000 + 17438.66667 = 17438.66667 -288.4848485x + x2 = 17438.66667 The x term is -288.4848485x. Take half its coefficient (-144.2424243). Square it (20805.87697) and add it to both sides. Add '20805.87697' to each side of the equation. -288.4848485x + 20805.87697 + x2 = 17438.66667 + 20805.87697 Reorder the terms: 20805.87697 + -288.4848485x + x2 = 17438.66667 + 20805.87697 Combine like terms: 17438.66667 + 20805.87697 = 38244.54364 20805.87697 + -288.4848485x + x2 = 38244.54364 Factor a perfect square on the left side: (x + -144.2424243)(x + -144.2424243) = 38244.54364 Calculate the square root of the right side: 195.562122202 Break this problem into two subproblems by setting (x + -144.2424243) equal to 195.562122202 and -195.562122202.Subproblem 1
x + -144.2424243 = 195.562122202 Simplifying x + -144.2424243 = 195.562122202 Reorder the terms: -144.2424243 + x = 195.562122202 Solving -144.2424243 + x = 195.562122202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '144.2424243' to each side of the equation. -144.2424243 + 144.2424243 + x = 195.562122202 + 144.2424243 Combine like terms: -144.2424243 + 144.2424243 = 0.0000000 0.0000000 + x = 195.562122202 + 144.2424243 x = 195.562122202 + 144.2424243 Combine like terms: 195.562122202 + 144.2424243 = 339.804546502 x = 339.804546502 Simplifying x = 339.804546502Subproblem 2
x + -144.2424243 = -195.562122202 Simplifying x + -144.2424243 = -195.562122202 Reorder the terms: -144.2424243 + x = -195.562122202 Solving -144.2424243 + x = -195.562122202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '144.2424243' to each side of the equation. -144.2424243 + 144.2424243 + x = -195.562122202 + 144.2424243 Combine like terms: -144.2424243 + 144.2424243 = 0.0000000 0.0000000 + x = -195.562122202 + 144.2424243 x = -195.562122202 + 144.2424243 Combine like terms: -195.562122202 + 144.2424243 = -51.319697902 x = -51.319697902 Simplifying x = -51.319697902Solution
The solution to the problem is based on the solutions from the subproblems. x = {339.804546502, -51.319697902}
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