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Simplifying x2 + 1.8x + -0.124 = 0 Reorder the terms: -0.124 + 1.8x + x2 = 0 Solving -0.124 + 1.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.124' to each side of the equation. -0.124 + 1.8x + 0.124 + x2 = 0 + 0.124 Reorder the terms: -0.124 + 0.124 + 1.8x + x2 = 0 + 0.124 Combine like terms: -0.124 + 0.124 = 0.000 0.000 + 1.8x + x2 = 0 + 0.124 1.8x + x2 = 0 + 0.124 Combine like terms: 0 + 0.124 = 0.124 1.8x + x2 = 0.124 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 = 0.124 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.124 + 0.81 Combine like terms: 0.124 + 0.81 = 0.934 0.81 + 1.8x + x2 = 0.934 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 0.934 Calculate the square root of the right side: 0.966436754 Break this problem into two subproblems by setting (x + 0.9) equal to 0.966436754 and -0.966436754.Subproblem 1
x + 0.9 = 0.966436754 Simplifying x + 0.9 = 0.966436754 Reorder the terms: 0.9 + x = 0.966436754 Solving 0.9 + x = 0.966436754 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 = 0.966436754 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.966436754 + -0.9 x = 0.966436754 + -0.9 Combine like terms: 0.966436754 + -0.9 = 0.066436754 x = 0.066436754 Simplifying x = 0.066436754Subproblem 2
x + 0.9 = -0.966436754 Simplifying x + 0.9 = -0.966436754 Reorder the terms: 0.9 + x = -0.966436754 Solving 0.9 + x = -0.966436754 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 = -0.966436754 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.966436754 + -0.9 x = -0.966436754 + -0.9 Combine like terms: -0.966436754 + -0.9 = -1.866436754 x = -1.866436754 Simplifying x = -1.866436754Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.066436754, -1.866436754}
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