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Simplifying 280 + -39.3x + x2 = 0 Solving 280 + -39.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-280' to each side of the equation. 280 + -39.3x + -280 + x2 = 0 + -280 Reorder the terms: 280 + -280 + -39.3x + x2 = 0 + -280 Combine like terms: 280 + -280 = 0 0 + -39.3x + x2 = 0 + -280 -39.3x + x2 = 0 + -280 Combine like terms: 0 + -280 = -280 -39.3x + x2 = -280 The x term is -39.3x. Take half its coefficient (-19.65). Square it (386.1225) and add it to both sides. Add '386.1225' to each side of the equation. -39.3x + 386.1225 + x2 = -280 + 386.1225 Reorder the terms: 386.1225 + -39.3x + x2 = -280 + 386.1225 Combine like terms: -280 + 386.1225 = 106.1225 386.1225 + -39.3x + x2 = 106.1225 Factor a perfect square on the left side: (x + -19.65)(x + -19.65) = 106.1225 Calculate the square root of the right side: 10.301577549 Break this problem into two subproblems by setting (x + -19.65) equal to 10.301577549 and -10.301577549.Subproblem 1
x + -19.65 = 10.301577549 Simplifying x + -19.65 = 10.301577549 Reorder the terms: -19.65 + x = 10.301577549 Solving -19.65 + x = 10.301577549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.65' to each side of the equation. -19.65 + 19.65 + x = 10.301577549 + 19.65 Combine like terms: -19.65 + 19.65 = 0.00 0.00 + x = 10.301577549 + 19.65 x = 10.301577549 + 19.65 Combine like terms: 10.301577549 + 19.65 = 29.951577549 x = 29.951577549 Simplifying x = 29.951577549Subproblem 2
x + -19.65 = -10.301577549 Simplifying x + -19.65 = -10.301577549 Reorder the terms: -19.65 + x = -10.301577549 Solving -19.65 + x = -10.301577549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.65' to each side of the equation. -19.65 + 19.65 + x = -10.301577549 + 19.65 Combine like terms: -19.65 + 19.65 = 0.00 0.00 + x = -10.301577549 + 19.65 x = -10.301577549 + 19.65 Combine like terms: -10.301577549 + 19.65 = 9.348422451 x = 9.348422451 Simplifying x = 9.348422451Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.951577549, 9.348422451}
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