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Simplifying x2 + -3x = -0.8776 + -1x Reorder the terms: -3x + x2 = -0.8776 + -1x Solving -3x + x2 = -0.8776 + -1x Solving for variable 'x'. Reorder the terms: 0.8776 + -3x + x + x2 = -0.8776 + -1x + 0.8776 + x Combine like terms: -3x + x = -2x 0.8776 + -2x + x2 = -0.8776 + -1x + 0.8776 + x Reorder the terms: 0.8776 + -2x + x2 = -0.8776 + 0.8776 + -1x + x Combine like terms: -0.8776 + 0.8776 = 0.0000 0.8776 + -2x + x2 = 0.0000 + -1x + x 0.8776 + -2x + x2 = -1x + x Combine like terms: -1x + x = 0 0.8776 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.8776' to each side of the equation. 0.8776 + -2x + -0.8776 + x2 = 0 + -0.8776 Reorder the terms: 0.8776 + -0.8776 + -2x + x2 = 0 + -0.8776 Combine like terms: 0.8776 + -0.8776 = 0.0000 0.0000 + -2x + x2 = 0 + -0.8776 -2x + x2 = 0 + -0.8776 Combine like terms: 0 + -0.8776 = -0.8776 -2x + x2 = -0.8776 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.8776 + 1 Reorder the terms: 1 + -2x + x2 = -0.8776 + 1 Combine like terms: -0.8776 + 1 = 0.1224 1 + -2x + x2 = 0.1224 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.1224 Calculate the square root of the right side: 0.349857114 Break this problem into two subproblems by setting (x + -1) equal to 0.349857114 and -0.349857114.Subproblem 1
x + -1 = 0.349857114 Simplifying x + -1 = 0.349857114 Reorder the terms: -1 + x = 0.349857114 Solving -1 + x = 0.349857114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.349857114 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.349857114 + 1 x = 0.349857114 + 1 Combine like terms: 0.349857114 + 1 = 1.349857114 x = 1.349857114 Simplifying x = 1.349857114Subproblem 2
x + -1 = -0.349857114 Simplifying x + -1 = -0.349857114 Reorder the terms: -1 + x = -0.349857114 Solving -1 + x = -0.349857114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.349857114 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.349857114 + 1 x = -0.349857114 + 1 Combine like terms: -0.349857114 + 1 = 0.650142886 x = 0.650142886 Simplifying x = 0.650142886Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.349857114, 0.650142886}
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