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Simplifying 60x2 + -341x = 259x + -25 Reorder the terms: -341x + 60x2 = 259x + -25 Reorder the terms: -341x + 60x2 = -25 + 259x Solving -341x + 60x2 = -25 + 259x Solving for variable 'x'. Reorder the terms: 25 + -341x + -259x + 60x2 = -25 + 259x + 25 + -259x Combine like terms: -341x + -259x = -600x 25 + -600x + 60x2 = -25 + 259x + 25 + -259x Reorder the terms: 25 + -600x + 60x2 = -25 + 25 + 259x + -259x Combine like terms: -25 + 25 = 0 25 + -600x + 60x2 = 0 + 259x + -259x 25 + -600x + 60x2 = 259x + -259x Combine like terms: 259x + -259x = 0 25 + -600x + 60x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -120x + 12x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -120x + 12x2)' equal to zero and attempt to solve: Simplifying 5 + -120x + 12x2 = 0 Solving 5 + -120x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + -10x + x2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + -10x + -0.4166666667 + x2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + -10x + x2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + -10x + x2 = 0 + -0.4166666667 -10x + x2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 -10x + x2 = -0.4166666667 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -0.4166666667 + 25 Reorder the terms: 25 + -10x + x2 = -0.4166666667 + 25 Combine like terms: -0.4166666667 + 25 = 24.5833333333 25 + -10x + x2 = 24.5833333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 24.5833333333 Calculate the square root of the right side: 4.95815826 Break this problem into two subproblems by setting (x + -5) equal to 4.95815826 and -4.95815826.Subproblem 1
x + -5 = 4.95815826 Simplifying x + -5 = 4.95815826 Reorder the terms: -5 + x = 4.95815826 Solving -5 + x = 4.95815826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.95815826 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.95815826 + 5 x = 4.95815826 + 5 Combine like terms: 4.95815826 + 5 = 9.95815826 x = 9.95815826 Simplifying x = 9.95815826Subproblem 2
x + -5 = -4.95815826 Simplifying x + -5 = -4.95815826 Reorder the terms: -5 + x = -4.95815826 Solving -5 + x = -4.95815826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.95815826 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.95815826 + 5 x = -4.95815826 + 5 Combine like terms: -4.95815826 + 5 = 0.04184174 x = 0.04184174 Simplifying x = 0.04184174Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.95815826, 0.04184174}Solution
x = {9.95815826, 0.04184174}
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