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Simplifying 0 = 25(100x + -5x2 + -6) Reorder the terms: 0 = 25(-6 + 100x + -5x2) 0 = (-6 * 25 + 100x * 25 + -5x2 * 25) 0 = (-150 + 2500x + -125x2) Solving 0 = -150 + 2500x + -125x2 Solving for variable 'x'. Combine like terms: 0 + 150 = 150 150 + -2500x + 125x2 = -150 + 2500x + -125x2 + 150 + -2500x + 125x2 Reorder the terms: 150 + -2500x + 125x2 = -150 + 150 + 2500x + -2500x + -125x2 + 125x2 Combine like terms: -150 + 150 = 0 150 + -2500x + 125x2 = 0 + 2500x + -2500x + -125x2 + 125x2 150 + -2500x + 125x2 = 2500x + -2500x + -125x2 + 125x2 Combine like terms: 2500x + -2500x = 0 150 + -2500x + 125x2 = 0 + -125x2 + 125x2 150 + -2500x + 125x2 = -125x2 + 125x2 Combine like terms: -125x2 + 125x2 = 0 150 + -2500x + 125x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(6 + -100x + 5x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(6 + -100x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + -100x + 5x2 = 0 Solving 6 + -100x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -20x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -20x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -20x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -20x + x2 = 0 + -1.2 -20x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -20x + x2 = -1.2 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -1.2 + 100 Reorder the terms: 100 + -20x + x2 = -1.2 + 100 Combine like terms: -1.2 + 100 = 98.8 100 + -20x + x2 = 98.8 Factor a perfect square on the left side: (x + -10)(x + -10) = 98.8 Calculate the square root of the right side: 9.939818912 Break this problem into two subproblems by setting (x + -10) equal to 9.939818912 and -9.939818912.Subproblem 1
x + -10 = 9.939818912 Simplifying x + -10 = 9.939818912 Reorder the terms: -10 + x = 9.939818912 Solving -10 + x = 9.939818912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.939818912 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.939818912 + 10 x = 9.939818912 + 10 Combine like terms: 9.939818912 + 10 = 19.939818912 x = 19.939818912 Simplifying x = 19.939818912Subproblem 2
x + -10 = -9.939818912 Simplifying x + -10 = -9.939818912 Reorder the terms: -10 + x = -9.939818912 Solving -10 + x = -9.939818912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.939818912 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.939818912 + 10 x = -9.939818912 + 10 Combine like terms: -9.939818912 + 10 = 0.060181088 x = 0.060181088 Simplifying x = 0.060181088Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.939818912, 0.060181088}Solution
x = {19.939818912, 0.060181088}
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