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Simplifying 2x2 + -3.1x + 0.42 = 0 Reorder the terms: 0.42 + -3.1x + 2x2 = 0 Solving 0.42 + -3.1x + 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'. 0.21 + -1.55x + x2 = 0 Move the constant term to the right: Add '-0.21' to each side of the equation. 0.21 + -1.55x + -0.21 + x2 = 0 + -0.21 Reorder the terms: 0.21 + -0.21 + -1.55x + x2 = 0 + -0.21 Combine like terms: 0.21 + -0.21 = 0.00 0.00 + -1.55x + x2 = 0 + -0.21 -1.55x + x2 = 0 + -0.21 Combine like terms: 0 + -0.21 = -0.21 -1.55x + x2 = -0.21 The x term is -1.55x. Take half its coefficient (-0.775). Square it (0.600625) and add it to both sides. Add '0.600625' to each side of the equation. -1.55x + 0.600625 + x2 = -0.21 + 0.600625 Reorder the terms: 0.600625 + -1.55x + x2 = -0.21 + 0.600625 Combine like terms: -0.21 + 0.600625 = 0.390625 0.600625 + -1.55x + x2 = 0.390625 Factor a perfect square on the left side: (x + -0.775)(x + -0.775) = 0.390625 Calculate the square root of the right side: 0.625 Break this problem into two subproblems by setting (x + -0.775) equal to 0.625 and -0.625.Subproblem 1
x + -0.775 = 0.625 Simplifying x + -0.775 = 0.625 Reorder the terms: -0.775 + x = 0.625 Solving -0.775 + x = 0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.775' to each side of the equation. -0.775 + 0.775 + x = 0.625 + 0.775 Combine like terms: -0.775 + 0.775 = 0.000 0.000 + x = 0.625 + 0.775 x = 0.625 + 0.775 Combine like terms: 0.625 + 0.775 = 1.4 x = 1.4 Simplifying x = 1.4Subproblem 2
x + -0.775 = -0.625 Simplifying x + -0.775 = -0.625 Reorder the terms: -0.775 + x = -0.625 Solving -0.775 + x = -0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.775' to each side of the equation. -0.775 + 0.775 + x = -0.625 + 0.775 Combine like terms: -0.775 + 0.775 = 0.000 0.000 + x = -0.625 + 0.775 x = -0.625 + 0.775 Combine like terms: -0.625 + 0.775 = 0.15 x = 0.15 Simplifying x = 0.15Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4, 0.15}
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