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Simplifying 0.00001(0.1659 + -1x + x2) = 0 (0.1659 * 0.00001 + -1x * 0.00001 + x2 * 0.00001) = 0 (0.000001659 + -0.00001x + 0.00001x2) = 0 Solving 0.000001659 + -0.00001x + 0.00001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.00001 the coefficient of the squared term: Divide each side by '0.00001'. 0.1659 + -1x + x2 = 0 Move the constant term to the right: Add '-0.1659' to each side of the equation. 0.1659 + -1x + -0.1659 + x2 = 0 + -0.1659 Reorder the terms: 0.1659 + -0.1659 + -1x + x2 = 0 + -0.1659 Combine like terms: 0.1659 + -0.1659 = 0.0000 0.0000 + -1x + x2 = 0 + -0.1659 -1x + x2 = 0 + -0.1659 Combine like terms: 0 + -0.1659 = -0.1659 -1x + x2 = -0.1659 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.1659 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.1659 + 0.25 Combine like terms: -0.1659 + 0.25 = 0.0841 0.25 + -1x + x2 = 0.0841 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.0841 Calculate the square root of the right side: 0.29 Break this problem into two subproblems by setting (x + -0.5) equal to 0.29 and -0.29.Subproblem 1
x + -0.5 = 0.29 Simplifying x + -0.5 = 0.29 Reorder the terms: -0.5 + x = 0.29 Solving -0.5 + x = 0.29 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.29 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.29 + 0.5 x = 0.29 + 0.5 Combine like terms: 0.29 + 0.5 = 0.79 x = 0.79 Simplifying x = 0.79Subproblem 2
x + -0.5 = -0.29 Simplifying x + -0.5 = -0.29 Reorder the terms: -0.5 + x = -0.29 Solving -0.5 + x = -0.29 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.29 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.29 + 0.5 x = -0.29 + 0.5 Combine like terms: -0.29 + 0.5 = 0.21 x = 0.21 Simplifying x = 0.21Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.79, 0.21}
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