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Simplifying 1.5 = -0.00009x2 + 0.0283x + 1.1233 Reorder the terms: 1.5 = 1.1233 + 0.0283x + -0.00009x2 Solving 1.5 = 1.1233 + 0.0283x + -0.00009x2 Solving for variable 'x'. Combine like terms: 1.5 + -1.1233 = 0.3767 0.3767 + -0.0283x + 0.00009x2 = 1.1233 + 0.0283x + -0.00009x2 + -1.1233 + -0.0283x + 0.00009x2 Reorder the terms: 0.3767 + -0.0283x + 0.00009x2 = 1.1233 + -1.1233 + 0.0283x + -0.0283x + -0.00009x2 + 0.00009x2 Combine like terms: 1.1233 + -1.1233 = 0.0000 0.3767 + -0.0283x + 0.00009x2 = 0.0000 + 0.0283x + -0.0283x + -0.00009x2 + 0.00009x2 0.3767 + -0.0283x + 0.00009x2 = 0.0283x + -0.0283x + -0.00009x2 + 0.00009x2 Combine like terms: 0.0283x + -0.0283x = 0.0000 0.3767 + -0.0283x + 0.00009x2 = 0.0000 + -0.00009x2 + 0.00009x2 0.3767 + -0.0283x + 0.00009x2 = -0.00009x2 + 0.00009x2 Combine like terms: -0.00009x2 + 0.00009x2 = 0.00000 0.3767 + -0.0283x + 0.00009x2 = 0.00000 Begin completing the square. Divide all terms by 0.00009 the coefficient of the squared term: Divide each side by '0.00009'. 4185.555556 + -314.4444444x + x2 = 0 Move the constant term to the right: Add '-4185.555556' to each side of the equation. 4185.555556 + -314.4444444x + -4185.555556 + x2 = 0 + -4185.555556 Reorder the terms: 4185.555556 + -4185.555556 + -314.4444444x + x2 = 0 + -4185.555556 Combine like terms: 4185.555556 + -4185.555556 = 0.000000 0.000000 + -314.4444444x + x2 = 0 + -4185.555556 -314.4444444x + x2 = 0 + -4185.555556 Combine like terms: 0 + -4185.555556 = -4185.555556 -314.4444444x + x2 = -4185.555556 The x term is -314.4444444x. Take half its coefficient (-157.2222222). Square it (24718.82715) and add it to both sides. Add '24718.82715' to each side of the equation. -314.4444444x + 24718.82715 + x2 = -4185.555556 + 24718.82715 Reorder the terms: 24718.82715 + -314.4444444x + x2 = -4185.555556 + 24718.82715 Combine like terms: -4185.555556 + 24718.82715 = 20533.271594 24718.82715 + -314.4444444x + x2 = 20533.271594 Factor a perfect square on the left side: (x + -157.2222222)(x + -157.2222222) = 20533.271594 Calculate the square root of the right side: 143.294352973 Break this problem into two subproblems by setting (x + -157.2222222) equal to 143.294352973 and -143.294352973.Subproblem 1
x + -157.2222222 = 143.294352973 Simplifying x + -157.2222222 = 143.294352973 Reorder the terms: -157.2222222 + x = 143.294352973 Solving -157.2222222 + x = 143.294352973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '157.2222222' to each side of the equation. -157.2222222 + 157.2222222 + x = 143.294352973 + 157.2222222 Combine like terms: -157.2222222 + 157.2222222 = 0.0000000 0.0000000 + x = 143.294352973 + 157.2222222 x = 143.294352973 + 157.2222222 Combine like terms: 143.294352973 + 157.2222222 = 300.516575173 x = 300.516575173 Simplifying x = 300.516575173Subproblem 2
x + -157.2222222 = -143.294352973 Simplifying x + -157.2222222 = -143.294352973 Reorder the terms: -157.2222222 + x = -143.294352973 Solving -157.2222222 + x = -143.294352973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '157.2222222' to each side of the equation. -157.2222222 + 157.2222222 + x = -143.294352973 + 157.2222222 Combine like terms: -157.2222222 + 157.2222222 = 0.0000000 0.0000000 + x = -143.294352973 + 157.2222222 x = -143.294352973 + 157.2222222 Combine like terms: -143.294352973 + 157.2222222 = 13.927869227 x = 13.927869227 Simplifying x = 13.927869227Solution
The solution to the problem is based on the solutions from the subproblems. x = {300.516575173, 13.927869227}
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