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Simplifying x2 + 17x + 29 = 0 Reorder the terms: 29 + 17x + x2 = 0 Solving 29 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 17x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 17x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 17x + x2 = 0 + -29 17x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 17x + x2 = -29 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -29 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -29 + 72.25 Combine like terms: -29 + 72.25 = 43.25 72.25 + 17x + x2 = 43.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + 8.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + 8.5 = 6.576473219 Simplifying x + 8.5 = 6.576473219 Reorder the terms: 8.5 + x = 6.576473219 Solving 8.5 + x = 6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 6.576473219 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 6.576473219 + -8.5 x = 6.576473219 + -8.5 Combine like terms: 6.576473219 + -8.5 = -1.923526781 x = -1.923526781 Simplifying x = -1.923526781Subproblem 2
x + 8.5 = -6.576473219 Simplifying x + 8.5 = -6.576473219 Reorder the terms: 8.5 + x = -6.576473219 Solving 8.5 + x = -6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -6.576473219 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -6.576473219 + -8.5 x = -6.576473219 + -8.5 Combine like terms: -6.576473219 + -8.5 = -15.076473219 x = -15.076473219 Simplifying x = -15.076473219Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.923526781, -15.076473219}
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