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Simplifying 82(0.006889 + -1x2) = 2x (0.006889 * 82 + -1x2 * 82) = 2x (0.564898 + -82x2) = 2x Solving 0.564898 + -82x2 = 2x Solving for variable 'x'. Reorder the terms: 0.564898 + -2x + -82x2 = 2x + -2x Combine like terms: 2x + -2x = 0 0.564898 + -2x + -82x2 = 0 Begin completing the square. Divide all terms by -82 the coefficient of the squared term: Divide each side by '-82'. -0.006889 + 0.0243902439x + x2 = 0 Move the constant term to the right: Add '0.006889' to each side of the equation. -0.006889 + 0.0243902439x + 0.006889 + x2 = 0 + 0.006889 Reorder the terms: -0.006889 + 0.006889 + 0.0243902439x + x2 = 0 + 0.006889 Combine like terms: -0.006889 + 0.006889 = 0.000000 0.000000 + 0.0243902439x + x2 = 0 + 0.006889 0.0243902439x + x2 = 0 + 0.006889 Combine like terms: 0 + 0.006889 = 0.006889 0.0243902439x + x2 = 0.006889 The x term is 0.0243902439x. Take half its coefficient (0.01219512195). Square it (0.0001487209994) and add it to both sides. Add '0.0001487209994' to each side of the equation. 0.0243902439x + 0.0001487209994 + x2 = 0.006889 + 0.0001487209994 Reorder the terms: 0.0001487209994 + 0.0243902439x + x2 = 0.006889 + 0.0001487209994 Combine like terms: 0.006889 + 0.0001487209994 = 0.0070377209994 0.0001487209994 + 0.0243902439x + x2 = 0.0070377209994 Factor a perfect square on the left side: (x + 0.01219512195)(x + 0.01219512195) = 0.0070377209994 Calculate the square root of the right side: 0.083891126 Break this problem into two subproblems by setting (x + 0.01219512195) equal to 0.083891126 and -0.083891126.Subproblem 1
x + 0.01219512195 = 0.083891126 Simplifying x + 0.01219512195 = 0.083891126 Reorder the terms: 0.01219512195 + x = 0.083891126 Solving 0.01219512195 + x = 0.083891126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01219512195' to each side of the equation. 0.01219512195 + -0.01219512195 + x = 0.083891126 + -0.01219512195 Combine like terms: 0.01219512195 + -0.01219512195 = 0.00000000000 0.00000000000 + x = 0.083891126 + -0.01219512195 x = 0.083891126 + -0.01219512195 Combine like terms: 0.083891126 + -0.01219512195 = 0.07169600405 x = 0.07169600405 Simplifying x = 0.07169600405Subproblem 2
x + 0.01219512195 = -0.083891126 Simplifying x + 0.01219512195 = -0.083891126 Reorder the terms: 0.01219512195 + x = -0.083891126 Solving 0.01219512195 + x = -0.083891126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01219512195' to each side of the equation. 0.01219512195 + -0.01219512195 + x = -0.083891126 + -0.01219512195 Combine like terms: 0.01219512195 + -0.01219512195 = 0.00000000000 0.00000000000 + x = -0.083891126 + -0.01219512195 x = -0.083891126 + -0.01219512195 Combine like terms: -0.083891126 + -0.01219512195 = -0.09608624795 x = -0.09608624795 Simplifying x = -0.09608624795Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.07169600405, -0.09608624795}
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