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Simplifying 46x2 + -56x + -63.75 = 0 Reorder the terms: -63.75 + -56x + 46x2 = 0 Solving -63.75 + -56x + 46x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 46 the coefficient of the squared term: Divide each side by '46'. -1.385869565 + -1.217391304x + x2 = 0 Move the constant term to the right: Add '1.385869565' to each side of the equation. -1.385869565 + -1.217391304x + 1.385869565 + x2 = 0 + 1.385869565 Reorder the terms: -1.385869565 + 1.385869565 + -1.217391304x + x2 = 0 + 1.385869565 Combine like terms: -1.385869565 + 1.385869565 = 0.000000000 0.000000000 + -1.217391304x + x2 = 0 + 1.385869565 -1.217391304x + x2 = 0 + 1.385869565 Combine like terms: 0 + 1.385869565 = 1.385869565 -1.217391304x + x2 = 1.385869565 The x term is -1.217391304x. Take half its coefficient (-0.608695652). Square it (0.3705103968) and add it to both sides. Add '0.3705103968' to each side of the equation. -1.217391304x + 0.3705103968 + x2 = 1.385869565 + 0.3705103968 Reorder the terms: 0.3705103968 + -1.217391304x + x2 = 1.385869565 + 0.3705103968 Combine like terms: 1.385869565 + 0.3705103968 = 1.7563799618 0.3705103968 + -1.217391304x + x2 = 1.7563799618 Factor a perfect square on the left side: (x + -0.608695652)(x + -0.608695652) = 1.7563799618 Calculate the square root of the right side: 1.325284861 Break this problem into two subproblems by setting (x + -0.608695652) equal to 1.325284861 and -1.325284861.Subproblem 1
x + -0.608695652 = 1.325284861 Simplifying x + -0.608695652 = 1.325284861 Reorder the terms: -0.608695652 + x = 1.325284861 Solving -0.608695652 + x = 1.325284861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.608695652' to each side of the equation. -0.608695652 + 0.608695652 + x = 1.325284861 + 0.608695652 Combine like terms: -0.608695652 + 0.608695652 = 0.000000000 0.000000000 + x = 1.325284861 + 0.608695652 x = 1.325284861 + 0.608695652 Combine like terms: 1.325284861 + 0.608695652 = 1.933980513 x = 1.933980513 Simplifying x = 1.933980513Subproblem 2
x + -0.608695652 = -1.325284861 Simplifying x + -0.608695652 = -1.325284861 Reorder the terms: -0.608695652 + x = -1.325284861 Solving -0.608695652 + x = -1.325284861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.608695652' to each side of the equation. -0.608695652 + 0.608695652 + x = -1.325284861 + 0.608695652 Combine like terms: -0.608695652 + 0.608695652 = 0.000000000 0.000000000 + x = -1.325284861 + 0.608695652 x = -1.325284861 + 0.608695652 Combine like terms: -1.325284861 + 0.608695652 = -0.716589209 x = -0.716589209 Simplifying x = -0.716589209Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.933980513, -0.716589209}
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