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Simplifying -0.33x2 + 95.2x + 5846.07 = 9.131000000 Reorder the terms: 5846.07 + 95.2x + -0.33x2 = 9.131000000 Solving 5846.07 + 95.2x + -0.33x2 = 9.131000000 Solving for variable 'x'. Reorder the terms: 5846.07 + -9.131000000 + 95.2x + -0.33x2 = 9.131000000 + -9.131000000 Combine like terms: 5846.07 + -9.131000000 = 5836.939 5836.939 + 95.2x + -0.33x2 = 9.131000000 + -9.131000000 Combine like terms: 9.131000000 + -9.131000000 = 0.000000000 5836.939 + 95.2x + -0.33x2 = 0.000000000 Begin completing the square. Divide all terms by -0.33 the coefficient of the squared term: Divide each side by '-0.33'. -17687.69394 + -288.4848485x + x2 = 0.0000000 Move the constant term to the right: Add '17687.69394' to each side of the equation. -17687.69394 + -288.4848485x + 17687.69394 + x2 = 0.0000000 + 17687.69394 Reorder the terms: -17687.69394 + 17687.69394 + -288.4848485x + x2 = 0.0000000 + 17687.69394 Combine like terms: -17687.69394 + 17687.69394 = 0.00000 0.00000 + -288.4848485x + x2 = 0.0000000 + 17687.69394 -288.4848485x + x2 = 0.0000000 + 17687.69394 Combine like terms: 0.0000000 + 17687.69394 = 17687.69394 -288.4848485x + x2 = 17687.69394 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 = 17687.69394 + 20805.87697 Reorder the terms: 20805.87697 + -288.4848485x + x2 = 17687.69394 + 20805.87697 Combine like terms: 17687.69394 + 20805.87697 = 38493.57091 20805.87697 + -288.4848485x + x2 = 38493.57091 Factor a perfect square on the left side: (x + -144.2424243)(x + -144.2424243) = 38493.57091 Calculate the square root of the right side: 196.197785181 Break this problem into two subproblems by setting (x + -144.2424243) equal to 196.197785181 and -196.197785181.Subproblem 1
x + -144.2424243 = 196.197785181 Simplifying x + -144.2424243 = 196.197785181 Reorder the terms: -144.2424243 + x = 196.197785181 Solving -144.2424243 + x = 196.197785181 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 = 196.197785181 + 144.2424243 Combine like terms: -144.2424243 + 144.2424243 = 0.0000000 0.0000000 + x = 196.197785181 + 144.2424243 x = 196.197785181 + 144.2424243 Combine like terms: 196.197785181 + 144.2424243 = 340.440209481 x = 340.440209481 Simplifying x = 340.440209481Subproblem 2
x + -144.2424243 = -196.197785181 Simplifying x + -144.2424243 = -196.197785181 Reorder the terms: -144.2424243 + x = -196.197785181 Solving -144.2424243 + x = -196.197785181 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 = -196.197785181 + 144.2424243 Combine like terms: -144.2424243 + 144.2424243 = 0.0000000 0.0000000 + x = -196.197785181 + 144.2424243 x = -196.197785181 + 144.2424243 Combine like terms: -196.197785181 + 144.2424243 = -51.955360881 x = -51.955360881 Simplifying x = -51.955360881Solution
The solution to the problem is based on the solutions from the subproblems. x = {340.440209481, -51.955360881}
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