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Simplifying -1x2 + -21x + 20 = 0 Reorder the terms: 20 + -21x + -1x2 = 0 Solving 20 + -21x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + 21x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 21x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 21x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 21x + x2 = 0 + 20 21x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 21x + x2 = 20 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = 20 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 20 + 110.25 Combine like terms: 20 + 110.25 = 130.25 110.25 + 21x + x2 = 130.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + 10.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + 10.5 = 11.412712211 Simplifying x + 10.5 = 11.412712211 Reorder the terms: 10.5 + x = 11.412712211 Solving 10.5 + x = 11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 11.412712211 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 11.412712211 + -10.5 x = 11.412712211 + -10.5 Combine like terms: 11.412712211 + -10.5 = 0.912712211 x = 0.912712211 Simplifying x = 0.912712211Subproblem 2
x + 10.5 = -11.412712211 Simplifying x + 10.5 = -11.412712211 Reorder the terms: 10.5 + x = -11.412712211 Solving 10.5 + x = -11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -11.412712211 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -11.412712211 + -10.5 x = -11.412712211 + -10.5 Combine like terms: -11.412712211 + -10.5 = -21.912712211 x = -21.912712211 Simplifying x = -21.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.912712211, -21.912712211}
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