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Simplifying 0.55078 = 0.0079x2 + -0.0534x Reorder the terms: 0.55078 = -0.0534x + 0.0079x2 Solving 0.55078 = -0.0534x + 0.0079x2 Solving for variable 'x'. Reorder the terms: 0.55078 + 0.0534x + -0.0079x2 = -0.0534x + 0.0534x + 0.0079x2 + -0.0079x2 Combine like terms: -0.0534x + 0.0534x = 0.0000 0.55078 + 0.0534x + -0.0079x2 = 0.0000 + 0.0079x2 + -0.0079x2 0.55078 + 0.0534x + -0.0079x2 = 0.0079x2 + -0.0079x2 Combine like terms: 0.0079x2 + -0.0079x2 = 0.0000 0.55078 + 0.0534x + -0.0079x2 = 0.0000 Begin completing the square. Divide all terms by -0.0079 the coefficient of the squared term: Divide each side by '-0.0079'. -69.71898734 + -6.759493671x + x2 = 0 Move the constant term to the right: Add '69.71898734' to each side of the equation. -69.71898734 + -6.759493671x + 69.71898734 + x2 = 0 + 69.71898734 Reorder the terms: -69.71898734 + 69.71898734 + -6.759493671x + x2 = 0 + 69.71898734 Combine like terms: -69.71898734 + 69.71898734 = 0.00000000 0.00000000 + -6.759493671x + x2 = 0 + 69.71898734 -6.759493671x + x2 = 0 + 69.71898734 Combine like terms: 0 + 69.71898734 = 69.71898734 -6.759493671x + x2 = 69.71898734 The x term is -6.759493671x. Take half its coefficient (-3.379746836). Square it (11.42268868) and add it to both sides. Add '11.42268868' to each side of the equation. -6.759493671x + 11.42268868 + x2 = 69.71898734 + 11.42268868 Reorder the terms: 11.42268868 + -6.759493671x + x2 = 69.71898734 + 11.42268868 Combine like terms: 69.71898734 + 11.42268868 = 81.14167602 11.42268868 + -6.759493671x + x2 = 81.14167602 Factor a perfect square on the left side: (x + -3.379746836)(x + -3.379746836) = 81.14167602 Calculate the square root of the right side: 9.007867451 Break this problem into two subproblems by setting (x + -3.379746836) equal to 9.007867451 and -9.007867451.Subproblem 1
x + -3.379746836 = 9.007867451 Simplifying x + -3.379746836 = 9.007867451 Reorder the terms: -3.379746836 + x = 9.007867451 Solving -3.379746836 + x = 9.007867451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.379746836' to each side of the equation. -3.379746836 + 3.379746836 + x = 9.007867451 + 3.379746836 Combine like terms: -3.379746836 + 3.379746836 = 0.000000000 0.000000000 + x = 9.007867451 + 3.379746836 x = 9.007867451 + 3.379746836 Combine like terms: 9.007867451 + 3.379746836 = 12.387614287 x = 12.387614287 Simplifying x = 12.387614287Subproblem 2
x + -3.379746836 = -9.007867451 Simplifying x + -3.379746836 = -9.007867451 Reorder the terms: -3.379746836 + x = -9.007867451 Solving -3.379746836 + x = -9.007867451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.379746836' to each side of the equation. -3.379746836 + 3.379746836 + x = -9.007867451 + 3.379746836 Combine like terms: -3.379746836 + 3.379746836 = 0.000000000 0.000000000 + x = -9.007867451 + 3.379746836 x = -9.007867451 + 3.379746836 Combine like terms: -9.007867451 + 3.379746836 = -5.628120615 x = -5.628120615 Simplifying x = -5.628120615Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.387614287, -5.628120615}
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