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Simplifying x2 + 38x + 17 = 0 Reorder the terms: 17 + 38x + x2 = 0 Solving 17 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 38x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 38x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 38x + x2 = 0 + -17 38x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 38x + x2 = -17 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 = -17 + 361 Reorder the terms: 361 + 38x + x2 = -17 + 361 Combine like terms: -17 + 361 = 344 361 + 38x + x2 = 344 Factor a perfect square on the left side: (x + 19)(x + 19) = 344 Calculate the square root of the right side: 18.547236991 Break this problem into two subproblems by setting (x + 19) equal to 18.547236991 and -18.547236991.Subproblem 1
x + 19 = 18.547236991 Simplifying x + 19 = 18.547236991 Reorder the terms: 19 + x = 18.547236991 Solving 19 + x = 18.547236991 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 = 18.547236991 + -19 Combine like terms: 19 + -19 = 0 0 + x = 18.547236991 + -19 x = 18.547236991 + -19 Combine like terms: 18.547236991 + -19 = -0.452763009 x = -0.452763009 Simplifying x = -0.452763009Subproblem 2
x + 19 = -18.547236991 Simplifying x + 19 = -18.547236991 Reorder the terms: 19 + x = -18.547236991 Solving 19 + x = -18.547236991 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 = -18.547236991 + -19 Combine like terms: 19 + -19 = 0 0 + x = -18.547236991 + -19 x = -18.547236991 + -19 Combine like terms: -18.547236991 + -19 = -37.547236991 x = -37.547236991 Simplifying x = -37.547236991Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.452763009, -37.547236991}
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