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Simplifying -2x2 + 20x = -82 Reorder the terms: 20x + -2x2 = -82 Solving 20x + -2x2 = -82 Solving for variable 'x'. Reorder the terms: 82 + 20x + -2x2 = -82 + 82 Combine like terms: -82 + 82 = 0 82 + 20x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(41 + 10x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying 41 + 10x + -1x2 = 0 Solving 41 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -41 + -10x + x2 = 0 Move the constant term to the right: Add '41' to each side of the equation. -41 + -10x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -10x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -10x + x2 = 0 + 41 -10x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -10x + x2 = 41 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 = 41 + 25 Reorder the terms: 25 + -10x + x2 = 41 + 25 Combine like terms: 41 + 25 = 66 25 + -10x + x2 = 66 Factor a perfect square on the left side: (x + -5)(x + -5) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + -5) equal to 8.124038405 and -8.124038405.Subproblem 1
x + -5 = 8.124038405 Simplifying x + -5 = 8.124038405 Reorder the terms: -5 + x = 8.124038405 Solving -5 + x = 8.124038405 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 = 8.124038405 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.124038405 + 5 x = 8.124038405 + 5 Combine like terms: 8.124038405 + 5 = 13.124038405 x = 13.124038405 Simplifying x = 13.124038405Subproblem 2
x + -5 = -8.124038405 Simplifying x + -5 = -8.124038405 Reorder the terms: -5 + x = -8.124038405 Solving -5 + x = -8.124038405 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 = -8.124038405 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.124038405 + 5 x = -8.124038405 + 5 Combine like terms: -8.124038405 + 5 = -3.124038405 x = -3.124038405 Simplifying x = -3.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.124038405, -3.124038405}Solution
x = {13.124038405, -3.124038405}
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