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Simplifying -1539x2 + 1539x + -100 = 0 Reorder the terms: -100 + 1539x + -1539x2 = 0 Solving -100 + 1539x + -1539x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1539 the coefficient of the squared term: Divide each side by '-1539'. 0.06497725796 + -1x + x2 = 0 Move the constant term to the right: Add '-0.06497725796' to each side of the equation. 0.06497725796 + -1x + -0.06497725796 + x2 = 0 + -0.06497725796 Reorder the terms: 0.06497725796 + -0.06497725796 + -1x + x2 = 0 + -0.06497725796 Combine like terms: 0.06497725796 + -0.06497725796 = 0.00000000000 0.00000000000 + -1x + x2 = 0 + -0.06497725796 -1x + x2 = 0 + -0.06497725796 Combine like terms: 0 + -0.06497725796 = -0.06497725796 -1x + x2 = -0.06497725796 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 = -0.06497725796 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.06497725796 + 0.25 Combine like terms: -0.06497725796 + 0.25 = 0.18502274204 0.25 + -1x + x2 = 0.18502274204 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.18502274204 Calculate the square root of the right side: 0.4301427 Break this problem into two subproblems by setting (x + -0.5) equal to 0.4301427 and -0.4301427.Subproblem 1
x + -0.5 = 0.4301427 Simplifying x + -0.5 = 0.4301427 Reorder the terms: -0.5 + x = 0.4301427 Solving -0.5 + x = 0.4301427 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 = 0.4301427 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.4301427 + 0.5 x = 0.4301427 + 0.5 Combine like terms: 0.4301427 + 0.5 = 0.9301427 x = 0.9301427 Simplifying x = 0.9301427Subproblem 2
x + -0.5 = -0.4301427 Simplifying x + -0.5 = -0.4301427 Reorder the terms: -0.5 + x = -0.4301427 Solving -0.5 + x = -0.4301427 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 = -0.4301427 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.4301427 + 0.5 x = -0.4301427 + 0.5 Combine like terms: -0.4301427 + 0.5 = 0.0698573 x = 0.0698573 Simplifying x = 0.0698573Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9301427, 0.0698573}
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