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Simplifying x2 + 0.42x + -0.1 = 0 Reorder the terms: -0.1 + 0.42x + x2 = 0 Solving -0.1 + 0.42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.42x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.42x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.42x + x2 = 0 + 0.1 0.42x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.42x + x2 = 0.1 The x term is 0.42x. Take half its coefficient (0.21). Square it (0.0441) and add it to both sides. Add '0.0441' to each side of the equation. 0.42x + 0.0441 + x2 = 0.1 + 0.0441 Reorder the terms: 0.0441 + 0.42x + x2 = 0.1 + 0.0441 Combine like terms: 0.1 + 0.0441 = 0.1441 0.0441 + 0.42x + x2 = 0.1441 Factor a perfect square on the left side: (x + 0.21)(x + 0.21) = 0.1441 Calculate the square root of the right side: 0.379605058 Break this problem into two subproblems by setting (x + 0.21) equal to 0.379605058 and -0.379605058.Subproblem 1
x + 0.21 = 0.379605058 Simplifying x + 0.21 = 0.379605058 Reorder the terms: 0.21 + x = 0.379605058 Solving 0.21 + x = 0.379605058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21' to each side of the equation. 0.21 + -0.21 + x = 0.379605058 + -0.21 Combine like terms: 0.21 + -0.21 = 0.00 0.00 + x = 0.379605058 + -0.21 x = 0.379605058 + -0.21 Combine like terms: 0.379605058 + -0.21 = 0.169605058 x = 0.169605058 Simplifying x = 0.169605058Subproblem 2
x + 0.21 = -0.379605058 Simplifying x + 0.21 = -0.379605058 Reorder the terms: 0.21 + x = -0.379605058 Solving 0.21 + x = -0.379605058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.21' to each side of the equation. 0.21 + -0.21 + x = -0.379605058 + -0.21 Combine like terms: 0.21 + -0.21 = 0.00 0.00 + x = -0.379605058 + -0.21 x = -0.379605058 + -0.21 Combine like terms: -0.379605058 + -0.21 = -0.589605058 x = -0.589605058 Simplifying x = -0.589605058Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.169605058, -0.589605058}
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