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Simplifying x2 + 19x + -19 = 0 Reorder the terms: -19 + 19x + x2 = 0 Solving -19 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 19x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 19x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 19x + x2 = 0 + 19 19x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 19x + x2 = 19 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 19 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 19 + 90.25 Combine like terms: 19 + 90.25 = 109.25 90.25 + 19x + x2 = 109.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 109.25 Calculate the square root of the right side: 10.45227248 Break this problem into two subproblems by setting (x + 9.5) equal to 10.45227248 and -10.45227248.Subproblem 1
x + 9.5 = 10.45227248 Simplifying x + 9.5 = 10.45227248 Reorder the terms: 9.5 + x = 10.45227248 Solving 9.5 + x = 10.45227248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 10.45227248 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 10.45227248 + -9.5 x = 10.45227248 + -9.5 Combine like terms: 10.45227248 + -9.5 = 0.95227248 x = 0.95227248 Simplifying x = 0.95227248Subproblem 2
x + 9.5 = -10.45227248 Simplifying x + 9.5 = -10.45227248 Reorder the terms: 9.5 + x = -10.45227248 Solving 9.5 + x = -10.45227248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -10.45227248 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -10.45227248 + -9.5 x = -10.45227248 + -9.5 Combine like terms: -10.45227248 + -9.5 = -19.95227248 x = -19.95227248 Simplifying x = -19.95227248Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.95227248, -19.95227248}
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