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Simplifying 0.2x2 + 0.31x + -0.15 = 0 Reorder the terms: -0.15 + 0.31x + 0.2x2 = 0 Solving -0.15 + 0.31x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -0.75 + 1.55x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.55x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.55x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.55x + x2 = 0 + 0.75 1.55x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.55x + x2 = 0.75 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 = 0.75 + 0.600625 Reorder the terms: 0.600625 + 1.55x + x2 = 0.75 + 0.600625 Combine like terms: 0.75 + 0.600625 = 1.350625 0.600625 + 1.55x + x2 = 1.350625 Factor a perfect square on the left side: (x + 0.775)(x + 0.775) = 1.350625 Calculate the square root of the right side: 1.16216393 Break this problem into two subproblems by setting (x + 0.775) equal to 1.16216393 and -1.16216393.Subproblem 1
x + 0.775 = 1.16216393 Simplifying x + 0.775 = 1.16216393 Reorder the terms: 0.775 + x = 1.16216393 Solving 0.775 + x = 1.16216393 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 = 1.16216393 + -0.775 Combine like terms: 0.775 + -0.775 = 0.000 0.000 + x = 1.16216393 + -0.775 x = 1.16216393 + -0.775 Combine like terms: 1.16216393 + -0.775 = 0.38716393 x = 0.38716393 Simplifying x = 0.38716393Subproblem 2
x + 0.775 = -1.16216393 Simplifying x + 0.775 = -1.16216393 Reorder the terms: 0.775 + x = -1.16216393 Solving 0.775 + x = -1.16216393 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 = -1.16216393 + -0.775 Combine like terms: 0.775 + -0.775 = 0.000 0.000 + x = -1.16216393 + -0.775 x = -1.16216393 + -0.775 Combine like terms: -1.16216393 + -0.775 = -1.93716393 x = -1.93716393 Simplifying x = -1.93716393Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.38716393, -1.93716393}
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