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Simplifying 0.942528755x2 + -1.20428204x + 0.015753284 = 0 Reorder the terms: 0.015753284 + -1.20428204x + 0.942528755x2 = 0 Solving 0.015753284 + -1.20428204x + 0.942528755x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.942528755 the coefficient of the squared term: Divide each side by '0.942528755'. 0.01671384975 + -1.277713845x + x2 = 0 Move the constant term to the right: Add '-0.01671384975' to each side of the equation. 0.01671384975 + -1.277713845x + -0.01671384975 + x2 = 0 + -0.01671384975 Reorder the terms: 0.01671384975 + -0.01671384975 + -1.277713845x + x2 = 0 + -0.01671384975 Combine like terms: 0.01671384975 + -0.01671384975 = 0.00000000000 0.00000000000 + -1.277713845x + x2 = 0 + -0.01671384975 -1.277713845x + x2 = 0 + -0.01671384975 Combine like terms: 0 + -0.01671384975 = -0.01671384975 -1.277713845x + x2 = -0.01671384975 The x term is -1.277713845x. Take half its coefficient (-0.6388569225). Square it (0.4081381674) and add it to both sides. Add '0.4081381674' to each side of the equation. -1.277713845x + 0.4081381674 + x2 = -0.01671384975 + 0.4081381674 Reorder the terms: 0.4081381674 + -1.277713845x + x2 = -0.01671384975 + 0.4081381674 Combine like terms: -0.01671384975 + 0.4081381674 = 0.39142431765 0.4081381674 + -1.277713845x + x2 = 0.39142431765 Factor a perfect square on the left side: (x + -0.6388569225)(x + -0.6388569225) = 0.39142431765 Calculate the square root of the right side: 0.625639127 Break this problem into two subproblems by setting (x + -0.6388569225) equal to 0.625639127 and -0.625639127.Subproblem 1
x + -0.6388569225 = 0.625639127 Simplifying x + -0.6388569225 = 0.625639127 Reorder the terms: -0.6388569225 + x = 0.625639127 Solving -0.6388569225 + x = 0.625639127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6388569225' to each side of the equation. -0.6388569225 + 0.6388569225 + x = 0.625639127 + 0.6388569225 Combine like terms: -0.6388569225 + 0.6388569225 = 0.0000000000 0.0000000000 + x = 0.625639127 + 0.6388569225 x = 0.625639127 + 0.6388569225 Combine like terms: 0.625639127 + 0.6388569225 = 1.2644960495 x = 1.2644960495 Simplifying x = 1.2644960495Subproblem 2
x + -0.6388569225 = -0.625639127 Simplifying x + -0.6388569225 = -0.625639127 Reorder the terms: -0.6388569225 + x = -0.625639127 Solving -0.6388569225 + x = -0.625639127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6388569225' to each side of the equation. -0.6388569225 + 0.6388569225 + x = -0.625639127 + 0.6388569225 Combine like terms: -0.6388569225 + 0.6388569225 = 0.0000000000 0.0000000000 + x = -0.625639127 + 0.6388569225 x = -0.625639127 + 0.6388569225 Combine like terms: -0.625639127 + 0.6388569225 = 0.0132177955 x = 0.0132177955 Simplifying x = 0.0132177955Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2644960495, 0.0132177955}
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