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Simplifying 34x2 + 1 = 36x Reorder the terms: 1 + 34x2 = 36x Solving 1 + 34x2 = 36x Solving for variable 'x'. Reorder the terms: 1 + -36x + 34x2 = 36x + -36x Combine like terms: 36x + -36x = 0 1 + -36x + 34x2 = 0 Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. 0.02941176471 + -1.058823529x + x2 = 0 Move the constant term to the right: Add '-0.02941176471' to each side of the equation. 0.02941176471 + -1.058823529x + -0.02941176471 + x2 = 0 + -0.02941176471 Reorder the terms: 0.02941176471 + -0.02941176471 + -1.058823529x + x2 = 0 + -0.02941176471 Combine like terms: 0.02941176471 + -0.02941176471 = 0.00000000000 0.00000000000 + -1.058823529x + x2 = 0 + -0.02941176471 -1.058823529x + x2 = 0 + -0.02941176471 Combine like terms: 0 + -0.02941176471 = -0.02941176471 -1.058823529x + x2 = -0.02941176471 The x term is -1.058823529x. Take half its coefficient (-0.5294117645). Square it (0.2802768164) and add it to both sides. Add '0.2802768164' to each side of the equation. -1.058823529x + 0.2802768164 + x2 = -0.02941176471 + 0.2802768164 Reorder the terms: 0.2802768164 + -1.058823529x + x2 = -0.02941176471 + 0.2802768164 Combine like terms: -0.02941176471 + 0.2802768164 = 0.25086505169 0.2802768164 + -1.058823529x + x2 = 0.25086505169 Factor a perfect square on the left side: (x + -0.5294117645)(x + -0.5294117645) = 0.25086505169 Calculate the square root of the right side: 0.500864305 Break this problem into two subproblems by setting (x + -0.5294117645) equal to 0.500864305 and -0.500864305.Subproblem 1
x + -0.5294117645 = 0.500864305 Simplifying x + -0.5294117645 = 0.500864305 Reorder the terms: -0.5294117645 + x = 0.500864305 Solving -0.5294117645 + x = 0.500864305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5294117645' to each side of the equation. -0.5294117645 + 0.5294117645 + x = 0.500864305 + 0.5294117645 Combine like terms: -0.5294117645 + 0.5294117645 = 0.0000000000 0.0000000000 + x = 0.500864305 + 0.5294117645 x = 0.500864305 + 0.5294117645 Combine like terms: 0.500864305 + 0.5294117645 = 1.0302760695 x = 1.0302760695 Simplifying x = 1.0302760695Subproblem 2
x + -0.5294117645 = -0.500864305 Simplifying x + -0.5294117645 = -0.500864305 Reorder the terms: -0.5294117645 + x = -0.500864305 Solving -0.5294117645 + x = -0.500864305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5294117645' to each side of the equation. -0.5294117645 + 0.5294117645 + x = -0.500864305 + 0.5294117645 Combine like terms: -0.5294117645 + 0.5294117645 = 0.0000000000 0.0000000000 + x = -0.500864305 + 0.5294117645 x = -0.500864305 + 0.5294117645 Combine like terms: -0.500864305 + 0.5294117645 = 0.0285474595 x = 0.0285474595 Simplifying x = 0.0285474595Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0302760695, 0.0285474595}
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