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Simplifying 0 = x2 + 20x + -81 Reorder the terms: 0 = -81 + 20x + x2 Solving 0 = -81 + 20x + x2 Solving for variable 'x'. Combine like terms: 0 + 81 = 81 81 + -20x + -1x2 = -81 + 20x + x2 + 81 + -20x + -1x2 Reorder the terms: 81 + -20x + -1x2 = -81 + 81 + 20x + -20x + x2 + -1x2 Combine like terms: -81 + 81 = 0 81 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 81 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 81 + -20x + -1x2 = 0 + x2 + -1x2 81 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 81 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + 20x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + 20x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 20x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 20x + x2 = 0 + 81 20x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 20x + x2 = 81 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 = 81 + 100 Reorder the terms: 100 + 20x + x2 = 81 + 100 Combine like terms: 81 + 100 = 181 100 + 20x + x2 = 181 Factor a perfect square on the left side: (x + 10)(x + 10) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (x + 10) equal to 13.453624047 and -13.453624047.Subproblem 1
x + 10 = 13.453624047 Simplifying x + 10 = 13.453624047 Reorder the terms: 10 + x = 13.453624047 Solving 10 + x = 13.453624047 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 = 13.453624047 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.453624047 + -10 x = 13.453624047 + -10 Combine like terms: 13.453624047 + -10 = 3.453624047 x = 3.453624047 Simplifying x = 3.453624047Subproblem 2
x + 10 = -13.453624047 Simplifying x + 10 = -13.453624047 Reorder the terms: 10 + x = -13.453624047 Solving 10 + x = -13.453624047 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 = -13.453624047 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.453624047 + -10 x = -13.453624047 + -10 Combine like terms: -13.453624047 + -10 = -23.453624047 x = -23.453624047 Simplifying x = -23.453624047Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.453624047, -23.453624047}
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