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Simplifying 3.1(x2) + -4x + 0.8 = 0 Reorder the terms: 0.8 + -4x + 3.1x2 = 0 Solving 0.8 + -4x + 3.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.1 the coefficient of the squared term: Divide each side by '3.1'. 0.2580645161 + -1.290322581x + x2 = 0 Move the constant term to the right: Add '-0.2580645161' to each side of the equation. 0.2580645161 + -1.290322581x + -0.2580645161 + x2 = 0 + -0.2580645161 Reorder the terms: 0.2580645161 + -0.2580645161 + -1.290322581x + x2 = 0 + -0.2580645161 Combine like terms: 0.2580645161 + -0.2580645161 = 0.0000000000 0.0000000000 + -1.290322581x + x2 = 0 + -0.2580645161 -1.290322581x + x2 = 0 + -0.2580645161 Combine like terms: 0 + -0.2580645161 = -0.2580645161 -1.290322581x + x2 = -0.2580645161 The x term is -1.290322581x. Take half its coefficient (-0.6451612905). Square it (0.4162330908) and add it to both sides. Add '0.4162330908' to each side of the equation. -1.290322581x + 0.4162330908 + x2 = -0.2580645161 + 0.4162330908 Reorder the terms: 0.4162330908 + -1.290322581x + x2 = -0.2580645161 + 0.4162330908 Combine like terms: -0.2580645161 + 0.4162330908 = 0.1581685747 0.4162330908 + -1.290322581x + x2 = 0.1581685747 Factor a perfect square on the left side: (x + -0.6451612905)(x + -0.6451612905) = 0.1581685747 Calculate the square root of the right side: 0.39770413 Break this problem into two subproblems by setting (x + -0.6451612905) equal to 0.39770413 and -0.39770413.Subproblem 1
x + -0.6451612905 = 0.39770413 Simplifying x + -0.6451612905 = 0.39770413 Reorder the terms: -0.6451612905 + x = 0.39770413 Solving -0.6451612905 + x = 0.39770413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6451612905' to each side of the equation. -0.6451612905 + 0.6451612905 + x = 0.39770413 + 0.6451612905 Combine like terms: -0.6451612905 + 0.6451612905 = 0.0000000000 0.0000000000 + x = 0.39770413 + 0.6451612905 x = 0.39770413 + 0.6451612905 Combine like terms: 0.39770413 + 0.6451612905 = 1.0428654205 x = 1.0428654205 Simplifying x = 1.0428654205Subproblem 2
x + -0.6451612905 = -0.39770413 Simplifying x + -0.6451612905 = -0.39770413 Reorder the terms: -0.6451612905 + x = -0.39770413 Solving -0.6451612905 + x = -0.39770413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6451612905' to each side of the equation. -0.6451612905 + 0.6451612905 + x = -0.39770413 + 0.6451612905 Combine like terms: -0.6451612905 + 0.6451612905 = 0.0000000000 0.0000000000 + x = -0.39770413 + 0.6451612905 x = -0.39770413 + 0.6451612905 Combine like terms: -0.39770413 + 0.6451612905 = 0.2474571605 x = 0.2474571605 Simplifying x = 0.2474571605Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0428654205, 0.2474571605}
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