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Simplifying x2 = 0.17784 + -1.8x Solving x2 = 0.17784 + -1.8x Solving for variable 'x'. Reorder the terms: -0.17784 + 1.8x + x2 = 0.17784 + -1.8x + -0.17784 + 1.8x Reorder the terms: -0.17784 + 1.8x + x2 = 0.17784 + -0.17784 + -1.8x + 1.8x Combine like terms: 0.17784 + -0.17784 = 0.00000 -0.17784 + 1.8x + x2 = 0.00000 + -1.8x + 1.8x -0.17784 + 1.8x + x2 = -1.8x + 1.8x Combine like terms: -1.8x + 1.8x = 0.0 -0.17784 + 1.8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.17784' to each side of the equation. -0.17784 + 1.8x + 0.17784 + x2 = 0.0 + 0.17784 Reorder the terms: -0.17784 + 0.17784 + 1.8x + x2 = 0.0 + 0.17784 Combine like terms: -0.17784 + 0.17784 = 0.00000 0.00000 + 1.8x + x2 = 0.0 + 0.17784 1.8x + x2 = 0.0 + 0.17784 Combine like terms: 0.0 + 0.17784 = 0.17784 1.8x + x2 = 0.17784 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 = 0.17784 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.17784 + 0.81 Combine like terms: 0.17784 + 0.81 = 0.98784 0.81 + 1.8x + x2 = 0.98784 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 0.98784 Calculate the square root of the right side: 0.993901404 Break this problem into two subproblems by setting (x + 0.9) equal to 0.993901404 and -0.993901404.Subproblem 1
x + 0.9 = 0.993901404 Simplifying x + 0.9 = 0.993901404 Reorder the terms: 0.9 + x = 0.993901404 Solving 0.9 + x = 0.993901404 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 = 0.993901404 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.993901404 + -0.9 x = 0.993901404 + -0.9 Combine like terms: 0.993901404 + -0.9 = 0.093901404 x = 0.093901404 Simplifying x = 0.093901404Subproblem 2
x + 0.9 = -0.993901404 Simplifying x + 0.9 = -0.993901404 Reorder the terms: 0.9 + x = -0.993901404 Solving 0.9 + x = -0.993901404 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 = -0.993901404 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.993901404 + -0.9 x = -0.993901404 + -0.9 Combine like terms: -0.993901404 + -0.9 = -1.893901404 x = -1.893901404 Simplifying x = -1.893901404Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.093901404, -1.893901404}
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