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Simplifying 0 = x2 + 20x + -19 Reorder the terms: 0 = -19 + 20x + x2 Solving 0 = -19 + 20x + x2 Solving for variable 'x'. Combine like terms: 0 + 19 = 19 19 + -20x + -1x2 = -19 + 20x + x2 + 19 + -20x + -1x2 Reorder the terms: 19 + -20x + -1x2 = -19 + 19 + 20x + -20x + x2 + -1x2 Combine like terms: -19 + 19 = 0 19 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 19 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 19 + -20x + -1x2 = 0 + x2 + -1x2 19 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 19 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + 20x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 20x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 20x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 20x + x2 = 0 + 19 20x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 20x + x2 = 19 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 = 19 + 100 Reorder the terms: 100 + 20x + x2 = 19 + 100 Combine like terms: 19 + 100 = 119 100 + 20x + x2 = 119 Factor a perfect square on the left side: (x + 10)(x + 10) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + 10) equal to 10.908712115 and -10.908712115.Subproblem 1
x + 10 = 10.908712115 Simplifying x + 10 = 10.908712115 Reorder the terms: 10 + x = 10.908712115 Solving 10 + x = 10.908712115 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 = 10.908712115 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.908712115 + -10 x = 10.908712115 + -10 Combine like terms: 10.908712115 + -10 = 0.908712115 x = 0.908712115 Simplifying x = 0.908712115Subproblem 2
x + 10 = -10.908712115 Simplifying x + 10 = -10.908712115 Reorder the terms: 10 + x = -10.908712115 Solving 10 + x = -10.908712115 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 = -10.908712115 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.908712115 + -10 x = -10.908712115 + -10 Combine like terms: -10.908712115 + -10 = -20.908712115 x = -20.908712115 Simplifying x = -20.908712115Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.908712115, -20.908712115}
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