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Simplifying x2 + -0.9x = -0.18 Reorder the terms: -0.9x + x2 = -0.18 Solving -0.9x + x2 = -0.18 Solving for variable 'x'. Reorder the terms: 0.18 + -0.9x + x2 = -0.18 + 0.18 Combine like terms: -0.18 + 0.18 = 0.00 0.18 + -0.9x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-0.18' to each side of the equation. 0.18 + -0.9x + -0.18 + x2 = 0.00 + -0.18 Reorder the terms: 0.18 + -0.18 + -0.9x + x2 = 0.00 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 0.00 + -0.9x + x2 = 0.00 + -0.18 -0.9x + x2 = 0.00 + -0.18 Combine like terms: 0.00 + -0.18 = -0.18 -0.9x + x2 = -0.18 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = -0.18 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = -0.18 + 0.2025 Combine like terms: -0.18 + 0.2025 = 0.0225 0.2025 + -0.9x + x2 = 0.0225 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = 0.0225 Calculate the square root of the right side: 0.15 Break this problem into two subproblems by setting (x + -0.45) equal to 0.15 and -0.15.Subproblem 1
x + -0.45 = 0.15 Simplifying x + -0.45 = 0.15 Reorder the terms: -0.45 + x = 0.15 Solving -0.45 + x = 0.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 0.15 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.15 + 0.45 x = 0.15 + 0.45 Combine like terms: 0.15 + 0.45 = 0.6 x = 0.6 Simplifying x = 0.6Subproblem 2
x + -0.45 = -0.15 Simplifying x + -0.45 = -0.15 Reorder the terms: -0.45 + x = -0.15 Solving -0.45 + x = -0.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -0.15 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.15 + 0.45 x = -0.15 + 0.45 Combine like terms: -0.15 + 0.45 = 0.3 x = 0.3 Simplifying x = 0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6, 0.3}
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