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Simplifying -0.5714x2 + 1.63x + -0.664255 = 0 Reorder the terms: -0.664255 + 1.63x + -0.5714x2 = 0 Solving -0.664255 + 1.63x + -0.5714x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5714 the coefficient of the squared term: Divide each side by '-0.5714'. 1.162504375 + -2.852642632x + x2 = 0 Move the constant term to the right: Add '-1.162504375' to each side of the equation. 1.162504375 + -2.852642632x + -1.162504375 + x2 = 0 + -1.162504375 Reorder the terms: 1.162504375 + -1.162504375 + -2.852642632x + x2 = 0 + -1.162504375 Combine like terms: 1.162504375 + -1.162504375 = 0.000000000 0.000000000 + -2.852642632x + x2 = 0 + -1.162504375 -2.852642632x + x2 = 0 + -1.162504375 Combine like terms: 0 + -1.162504375 = -1.162504375 -2.852642632x + x2 = -1.162504375 The x term is -2.852642632x. Take half its coefficient (-1.426321316). Square it (2.034392496) and add it to both sides. Add '2.034392496' to each side of the equation. -2.852642632x + 2.034392496 + x2 = -1.162504375 + 2.034392496 Reorder the terms: 2.034392496 + -2.852642632x + x2 = -1.162504375 + 2.034392496 Combine like terms: -1.162504375 + 2.034392496 = 0.871888121 2.034392496 + -2.852642632x + x2 = 0.871888121 Factor a perfect square on the left side: (x + -1.426321316)(x + -1.426321316) = 0.871888121 Calculate the square root of the right side: 0.933749496 Break this problem into two subproblems by setting (x + -1.426321316) equal to 0.933749496 and -0.933749496.Subproblem 1
x + -1.426321316 = 0.933749496 Simplifying x + -1.426321316 = 0.933749496 Reorder the terms: -1.426321316 + x = 0.933749496 Solving -1.426321316 + x = 0.933749496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.426321316' to each side of the equation. -1.426321316 + 1.426321316 + x = 0.933749496 + 1.426321316 Combine like terms: -1.426321316 + 1.426321316 = 0.000000000 0.000000000 + x = 0.933749496 + 1.426321316 x = 0.933749496 + 1.426321316 Combine like terms: 0.933749496 + 1.426321316 = 2.360070812 x = 2.360070812 Simplifying x = 2.360070812Subproblem 2
x + -1.426321316 = -0.933749496 Simplifying x + -1.426321316 = -0.933749496 Reorder the terms: -1.426321316 + x = -0.933749496 Solving -1.426321316 + x = -0.933749496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.426321316' to each side of the equation. -1.426321316 + 1.426321316 + x = -0.933749496 + 1.426321316 Combine like terms: -1.426321316 + 1.426321316 = 0.000000000 0.000000000 + x = -0.933749496 + 1.426321316 x = -0.933749496 + 1.426321316 Combine like terms: -0.933749496 + 1.426321316 = 0.49257182 x = 0.49257182 Simplifying x = 0.49257182Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.360070812, 0.49257182}
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