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Simplifying 10x2 + -1015x + 100 = 0 Reorder the terms: 100 + -1015x + 10x2 = 0 Solving 100 + -1015x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(20 + -203x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(20 + -203x + 2x2)' equal to zero and attempt to solve: Simplifying 20 + -203x + 2x2 = 0 Solving 20 + -203x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + -101.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -101.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -101.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -101.5x + x2 = 0 + -10 -101.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -101.5x + x2 = -10 The x term is -101.5x. Take half its coefficient (-50.75). Square it (2575.5625) and add it to both sides. Add '2575.5625' to each side of the equation. -101.5x + 2575.5625 + x2 = -10 + 2575.5625 Reorder the terms: 2575.5625 + -101.5x + x2 = -10 + 2575.5625 Combine like terms: -10 + 2575.5625 = 2565.5625 2575.5625 + -101.5x + x2 = 2565.5625 Factor a perfect square on the left side: (x + -50.75)(x + -50.75) = 2565.5625 Calculate the square root of the right side: 50.651382015 Break this problem into two subproblems by setting (x + -50.75) equal to 50.651382015 and -50.651382015.Subproblem 1
x + -50.75 = 50.651382015 Simplifying x + -50.75 = 50.651382015 Reorder the terms: -50.75 + x = 50.651382015 Solving -50.75 + x = 50.651382015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50.75' to each side of the equation. -50.75 + 50.75 + x = 50.651382015 + 50.75 Combine like terms: -50.75 + 50.75 = 0.00 0.00 + x = 50.651382015 + 50.75 x = 50.651382015 + 50.75 Combine like terms: 50.651382015 + 50.75 = 101.401382015 x = 101.401382015 Simplifying x = 101.401382015Subproblem 2
x + -50.75 = -50.651382015 Simplifying x + -50.75 = -50.651382015 Reorder the terms: -50.75 + x = -50.651382015 Solving -50.75 + x = -50.651382015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50.75' to each side of the equation. -50.75 + 50.75 + x = -50.651382015 + 50.75 Combine like terms: -50.75 + 50.75 = 0.00 0.00 + x = -50.651382015 + 50.75 x = -50.651382015 + 50.75 Combine like terms: -50.651382015 + 50.75 = 0.098617985 x = 0.098617985 Simplifying x = 0.098617985Solution
The solution to the problem is based on the solutions from the subproblems. x = {101.401382015, 0.098617985}Solution
x = {101.401382015, 0.098617985}
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