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Simplifying -1x2 + -1.8x + 0.11286 = 0 Reorder the terms: 0.11286 + -1.8x + -1x2 = 0 Solving 0.11286 + -1.8x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.11286 + 1.8x + x2 = 0 Move the constant term to the right: Add '0.11286' to each side of the equation. -0.11286 + 1.8x + 0.11286 + x2 = 0 + 0.11286 Reorder the terms: -0.11286 + 0.11286 + 1.8x + x2 = 0 + 0.11286 Combine like terms: -0.11286 + 0.11286 = 0.00000 0.00000 + 1.8x + x2 = 0 + 0.11286 1.8x + x2 = 0 + 0.11286 Combine like terms: 0 + 0.11286 = 0.11286 1.8x + x2 = 0.11286 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 0.11286 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.11286 + 0.81 Combine like terms: 0.11286 + 0.81 = 0.92286 0.81 + 1.8x + x2 = 0.92286 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 0.92286 Calculate the square root of the right side: 0.960656026 Break this problem into two subproblems by setting (x + 0.9) equal to 0.960656026 and -0.960656026.Subproblem 1
x + 0.9 = 0.960656026 Simplifying x + 0.9 = 0.960656026 Reorder the terms: 0.9 + x = 0.960656026 Solving 0.9 + x = 0.960656026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 0.960656026 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.960656026 + -0.9 x = 0.960656026 + -0.9 Combine like terms: 0.960656026 + -0.9 = 0.060656026 x = 0.060656026 Simplifying x = 0.060656026Subproblem 2
x + 0.9 = -0.960656026 Simplifying x + 0.9 = -0.960656026 Reorder the terms: 0.9 + x = -0.960656026 Solving 0.9 + x = -0.960656026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -0.960656026 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.960656026 + -0.9 x = -0.960656026 + -0.9 Combine like terms: -0.960656026 + -0.9 = -1.860656026 x = -1.860656026 Simplifying x = -1.860656026Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.060656026, -1.860656026}
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