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Simplifying x2 + 19x + -34 = 0 Reorder the terms: -34 + 19x + x2 = 0 Solving -34 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 19x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 19x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 19x + x2 = 0 + 34 19x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 19x + x2 = 34 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 = 34 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 34 + 90.25 Combine like terms: 34 + 90.25 = 124.25 90.25 + 19x + x2 = 124.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (x + 9.5) equal to 11.146748405 and -11.146748405.Subproblem 1
x + 9.5 = 11.146748405 Simplifying x + 9.5 = 11.146748405 Reorder the terms: 9.5 + x = 11.146748405 Solving 9.5 + x = 11.146748405 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 = 11.146748405 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 11.146748405 + -9.5 x = 11.146748405 + -9.5 Combine like terms: 11.146748405 + -9.5 = 1.646748405 x = 1.646748405 Simplifying x = 1.646748405Subproblem 2
x + 9.5 = -11.146748405 Simplifying x + 9.5 = -11.146748405 Reorder the terms: 9.5 + x = -11.146748405 Solving 9.5 + x = -11.146748405 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 = -11.146748405 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -11.146748405 + -9.5 x = -11.146748405 + -9.5 Combine like terms: -11.146748405 + -9.5 = -20.646748405 x = -20.646748405 Simplifying x = -20.646748405Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.646748405, -20.646748405}
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