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Simplifying x2 + 19x + -39 = 0 Reorder the terms: -39 + 19x + x2 = 0 Solving -39 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 19x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 19x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 19x + x2 = 0 + 39 19x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 19x + x2 = 39 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 = 39 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 39 + 90.25 Combine like terms: 39 + 90.25 = 129.25 90.25 + 19x + x2 = 129.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 129.25 Calculate the square root of the right side: 11.368817001 Break this problem into two subproblems by setting (x + 9.5) equal to 11.368817001 and -11.368817001.Subproblem 1
x + 9.5 = 11.368817001 Simplifying x + 9.5 = 11.368817001 Reorder the terms: 9.5 + x = 11.368817001 Solving 9.5 + x = 11.368817001 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 = 11.368817001 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 11.368817001 + -9.5 x = 11.368817001 + -9.5 Combine like terms: 11.368817001 + -9.5 = 1.868817001 x = 1.868817001 Simplifying x = 1.868817001Subproblem 2
x + 9.5 = -11.368817001 Simplifying x + 9.5 = -11.368817001 Reorder the terms: 9.5 + x = -11.368817001 Solving 9.5 + x = -11.368817001 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 = -11.368817001 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -11.368817001 + -9.5 x = -11.368817001 + -9.5 Combine like terms: -11.368817001 + -9.5 = -20.868817001 x = -20.868817001 Simplifying x = -20.868817001Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.868817001, -20.868817001}
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