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Simplifying -1.9 = 8.816x + (-4.9) * x2 Solving -1.9 = 8.816x + -4.9x2 Solving for variable 'x'. Reorder the terms: -1.9 + -8.816x + 4.9x2 = 8.816x + -8.816x + -4.9x2 + 4.9x2 Combine like terms: 8.816x + -8.816x = 0.000 -1.9 + -8.816x + 4.9x2 = 0.000 + -4.9x2 + 4.9x2 -1.9 + -8.816x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -1.9 + -8.816x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.387755102 + -1.799183673x + x2 = 0 Move the constant term to the right: Add '0.387755102' to each side of the equation. -0.387755102 + -1.799183673x + 0.387755102 + x2 = 0 + 0.387755102 Reorder the terms: -0.387755102 + 0.387755102 + -1.799183673x + x2 = 0 + 0.387755102 Combine like terms: -0.387755102 + 0.387755102 = 0.000000000 0.000000000 + -1.799183673x + x2 = 0 + 0.387755102 -1.799183673x + x2 = 0 + 0.387755102 Combine like terms: 0 + 0.387755102 = 0.387755102 -1.799183673x + x2 = 0.387755102 The x term is -1.799183673x. Take half its coefficient (-0.8995918365). Square it (0.8092654723) and add it to both sides. Add '0.8092654723' to each side of the equation. -1.799183673x + 0.8092654723 + x2 = 0.387755102 + 0.8092654723 Reorder the terms: 0.8092654723 + -1.799183673x + x2 = 0.387755102 + 0.8092654723 Combine like terms: 0.387755102 + 0.8092654723 = 1.1970205743 0.8092654723 + -1.799183673x + x2 = 1.1970205743 Factor a perfect square on the left side: (x + -0.8995918365)(x + -0.8995918365) = 1.1970205743 Calculate the square root of the right side: 1.094084354 Break this problem into two subproblems by setting (x + -0.8995918365) equal to 1.094084354 and -1.094084354.Subproblem 1
x + -0.8995918365 = 1.094084354 Simplifying x + -0.8995918365 = 1.094084354 Reorder the terms: -0.8995918365 + x = 1.094084354 Solving -0.8995918365 + x = 1.094084354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8995918365' to each side of the equation. -0.8995918365 + 0.8995918365 + x = 1.094084354 + 0.8995918365 Combine like terms: -0.8995918365 + 0.8995918365 = 0.0000000000 0.0000000000 + x = 1.094084354 + 0.8995918365 x = 1.094084354 + 0.8995918365 Combine like terms: 1.094084354 + 0.8995918365 = 1.9936761905 x = 1.9936761905 Simplifying x = 1.9936761905Subproblem 2
x + -0.8995918365 = -1.094084354 Simplifying x + -0.8995918365 = -1.094084354 Reorder the terms: -0.8995918365 + x = -1.094084354 Solving -0.8995918365 + x = -1.094084354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8995918365' to each side of the equation. -0.8995918365 + 0.8995918365 + x = -1.094084354 + 0.8995918365 Combine like terms: -0.8995918365 + 0.8995918365 = 0.0000000000 0.0000000000 + x = -1.094084354 + 0.8995918365 x = -1.094084354 + 0.8995918365 Combine like terms: -1.094084354 + 0.8995918365 = -0.1944925175 x = -0.1944925175 Simplifying x = -0.1944925175Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9936761905, -0.1944925175}
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