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Simplifying 1.3x2 + -3.306x = 0.94221 Reorder the terms: -3.306x + 1.3x2 = 0.94221 Solving -3.306x + 1.3x2 = 0.94221 Solving for variable 'x'. Reorder the terms: -0.94221 + -3.306x + 1.3x2 = 0.94221 + -0.94221 Combine like terms: 0.94221 + -0.94221 = 0.00000 -0.94221 + -3.306x + 1.3x2 = 0.00000 Begin completing the square. Divide all terms by 1.3 the coefficient of the squared term: Divide each side by '1.3'. -0.7247769231 + -2.543076923x + x2 = 0.0000 Move the constant term to the right: Add '0.7247769231' to each side of the equation. -0.7247769231 + -2.543076923x + 0.7247769231 + x2 = 0.0000 + 0.7247769231 Reorder the terms: -0.7247769231 + 0.7247769231 + -2.543076923x + x2 = 0.0000 + 0.7247769231 Combine like terms: -0.7247769231 + 0.7247769231 = 0.0000000000 0.0000000000 + -2.543076923x + x2 = 0.0000 + 0.7247769231 -2.543076923x + x2 = 0.0000 + 0.7247769231 Combine like terms: 0.0000 + 0.7247769231 = 0.7247769231 -2.543076923x + x2 = 0.7247769231 The x term is -2.543076923x. Take half its coefficient (-1.271538462). Square it (1.616810060) and add it to both sides. Add '1.616810060' to each side of the equation. -2.543076923x + 1.616810060 + x2 = 0.7247769231 + 1.616810060 Reorder the terms: 1.616810060 + -2.543076923x + x2 = 0.7247769231 + 1.616810060 Combine like terms: 0.7247769231 + 1.616810060 = 2.3415869831 1.616810060 + -2.543076923x + x2 = 2.3415869831 Factor a perfect square on the left side: (x + -1.271538462)(x + -1.271538462) = 2.3415869831 Calculate the square root of the right side: 1.530224488 Break this problem into two subproblems by setting (x + -1.271538462) equal to 1.530224488 and -1.530224488.Subproblem 1
x + -1.271538462 = 1.530224488 Simplifying x + -1.271538462 = 1.530224488 Reorder the terms: -1.271538462 + x = 1.530224488 Solving -1.271538462 + x = 1.530224488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.271538462' to each side of the equation. -1.271538462 + 1.271538462 + x = 1.530224488 + 1.271538462 Combine like terms: -1.271538462 + 1.271538462 = 0.000000000 0.000000000 + x = 1.530224488 + 1.271538462 x = 1.530224488 + 1.271538462 Combine like terms: 1.530224488 + 1.271538462 = 2.80176295 x = 2.80176295 Simplifying x = 2.80176295Subproblem 2
x + -1.271538462 = -1.530224488 Simplifying x + -1.271538462 = -1.530224488 Reorder the terms: -1.271538462 + x = -1.530224488 Solving -1.271538462 + x = -1.530224488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.271538462' to each side of the equation. -1.271538462 + 1.271538462 + x = -1.530224488 + 1.271538462 Combine like terms: -1.271538462 + 1.271538462 = 0.000000000 0.000000000 + x = -1.530224488 + 1.271538462 x = -1.530224488 + 1.271538462 Combine like terms: -1.530224488 + 1.271538462 = -0.258686026 x = -0.258686026 Simplifying x = -0.258686026Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.80176295, -0.258686026}
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