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Simplifying 24x2 + -39 = -26x Reorder the terms: -39 + 24x2 = -26x Solving -39 + 24x2 = -26x Solving for variable 'x'. Reorder the terms: -39 + 26x + 24x2 = -26x + 26x Combine like terms: -26x + 26x = 0 -39 + 26x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -1.625 + 1.083333333x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 1.083333333x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 1.083333333x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 1.083333333x + x2 = 0 + 1.625 1.083333333x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 1.083333333x + x2 = 1.625 The x term is 1.083333333x. Take half its coefficient (0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. 1.083333333x + 0.2934027776 + x2 = 1.625 + 0.2934027776 Reorder the terms: 0.2934027776 + 1.083333333x + x2 = 1.625 + 0.2934027776 Combine like terms: 1.625 + 0.2934027776 = 1.9184027776 0.2934027776 + 1.083333333x + x2 = 1.9184027776 Factor a perfect square on the left side: (x + 0.5416666665)(x + 0.5416666665) = 1.9184027776 Calculate the square root of the right side: 1.385064178 Break this problem into two subproblems by setting (x + 0.5416666665) equal to 1.385064178 and -1.385064178.Subproblem 1
x + 0.5416666665 = 1.385064178 Simplifying x + 0.5416666665 = 1.385064178 Reorder the terms: 0.5416666665 + x = 1.385064178 Solving 0.5416666665 + x = 1.385064178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5416666665' to each side of the equation. 0.5416666665 + -0.5416666665 + x = 1.385064178 + -0.5416666665 Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000 0.0000000000 + x = 1.385064178 + -0.5416666665 x = 1.385064178 + -0.5416666665 Combine like terms: 1.385064178 + -0.5416666665 = 0.8433975115 x = 0.8433975115 Simplifying x = 0.8433975115Subproblem 2
x + 0.5416666665 = -1.385064178 Simplifying x + 0.5416666665 = -1.385064178 Reorder the terms: 0.5416666665 + x = -1.385064178 Solving 0.5416666665 + x = -1.385064178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5416666665' to each side of the equation. 0.5416666665 + -0.5416666665 + x = -1.385064178 + -0.5416666665 Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000 0.0000000000 + x = -1.385064178 + -0.5416666665 x = -1.385064178 + -0.5416666665 Combine like terms: -1.385064178 + -0.5416666665 = -1.9267308445 x = -1.9267308445 Simplifying x = -1.9267308445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8433975115, -1.9267308445}
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