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Simplifying 2x2 + 0.31x + -0.15 = 0 Reorder the terms: -0.15 + 0.31x + 2x2 = 0 Solving -0.15 + 0.31x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.075 + 0.155x + x2 = 0 Move the constant term to the right: Add '0.075' to each side of the equation. -0.075 + 0.155x + 0.075 + x2 = 0 + 0.075 Reorder the terms: -0.075 + 0.075 + 0.155x + x2 = 0 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + 0.155x + x2 = 0 + 0.075 0.155x + x2 = 0 + 0.075 Combine like terms: 0 + 0.075 = 0.075 0.155x + x2 = 0.075 The x term is 0.155x. Take half its coefficient (0.0775). Square it (0.00600625) and add it to both sides. Add '0.00600625' to each side of the equation. 0.155x + 0.00600625 + x2 = 0.075 + 0.00600625 Reorder the terms: 0.00600625 + 0.155x + x2 = 0.075 + 0.00600625 Combine like terms: 0.075 + 0.00600625 = 0.08100625 0.00600625 + 0.155x + x2 = 0.08100625 Factor a perfect square on the left side: (x + 0.0775)(x + 0.0775) = 0.08100625 Calculate the square root of the right side: 0.284615969 Break this problem into two subproblems by setting (x + 0.0775) equal to 0.284615969 and -0.284615969.Subproblem 1
x + 0.0775 = 0.284615969 Simplifying x + 0.0775 = 0.284615969 Reorder the terms: 0.0775 + x = 0.284615969 Solving 0.0775 + x = 0.284615969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0775' to each side of the equation. 0.0775 + -0.0775 + x = 0.284615969 + -0.0775 Combine like terms: 0.0775 + -0.0775 = 0.0000 0.0000 + x = 0.284615969 + -0.0775 x = 0.284615969 + -0.0775 Combine like terms: 0.284615969 + -0.0775 = 0.207115969 x = 0.207115969 Simplifying x = 0.207115969Subproblem 2
x + 0.0775 = -0.284615969 Simplifying x + 0.0775 = -0.284615969 Reorder the terms: 0.0775 + x = -0.284615969 Solving 0.0775 + x = -0.284615969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0775' to each side of the equation. 0.0775 + -0.0775 + x = -0.284615969 + -0.0775 Combine like terms: 0.0775 + -0.0775 = 0.0000 0.0000 + x = -0.284615969 + -0.0775 x = -0.284615969 + -0.0775 Combine like terms: -0.284615969 + -0.0775 = -0.362115969 x = -0.362115969 Simplifying x = -0.362115969Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.207115969, -0.362115969}
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