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Simplifying x2 + -38x + 260 = 0 Reorder the terms: 260 + -38x + x2 = 0 Solving 260 + -38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-260' to each side of the equation. 260 + -38x + -260 + x2 = 0 + -260 Reorder the terms: 260 + -260 + -38x + x2 = 0 + -260 Combine like terms: 260 + -260 = 0 0 + -38x + x2 = 0 + -260 -38x + x2 = 0 + -260 Combine like terms: 0 + -260 = -260 -38x + x2 = -260 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = -260 + 361 Reorder the terms: 361 + -38x + x2 = -260 + 361 Combine like terms: -260 + 361 = 101 361 + -38x + x2 = 101 Factor a perfect square on the left side: (x + -19)(x + -19) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + -19) equal to 10.049875621 and -10.049875621.Subproblem 1
x + -19 = 10.049875621 Simplifying x + -19 = 10.049875621 Reorder the terms: -19 + x = 10.049875621 Solving -19 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 10.049875621 + 19 Combine like terms: -19 + 19 = 0 0 + x = 10.049875621 + 19 x = 10.049875621 + 19 Combine like terms: 10.049875621 + 19 = 29.049875621 x = 29.049875621 Simplifying x = 29.049875621Subproblem 2
x + -19 = -10.049875621 Simplifying x + -19 = -10.049875621 Reorder the terms: -19 + x = -10.049875621 Solving -19 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -10.049875621 + 19 Combine like terms: -19 + 19 = 0 0 + x = -10.049875621 + 19 x = -10.049875621 + 19 Combine like terms: -10.049875621 + 19 = 8.950124379 x = 8.950124379 Simplifying x = 8.950124379Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.049875621, 8.950124379}
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