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Simplifying x2 + 32x + 29 = 0 Reorder the terms: 29 + 32x + x2 = 0 Solving 29 + 32x + 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 + 32x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 32x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 32x + x2 = 0 + -29 32x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 32x + x2 = -29 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -29 + 256 Reorder the terms: 256 + 32x + x2 = -29 + 256 Combine like terms: -29 + 256 = 227 256 + 32x + x2 = 227 Factor a perfect square on the left side: (x + 16)(x + 16) = 227 Calculate the square root of the right side: 15.066519173 Break this problem into two subproblems by setting (x + 16) equal to 15.066519173 and -15.066519173.Subproblem 1
x + 16 = 15.066519173 Simplifying x + 16 = 15.066519173 Reorder the terms: 16 + x = 15.066519173 Solving 16 + x = 15.066519173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 15.066519173 + -16 Combine like terms: 16 + -16 = 0 0 + x = 15.066519173 + -16 x = 15.066519173 + -16 Combine like terms: 15.066519173 + -16 = -0.933480827 x = -0.933480827 Simplifying x = -0.933480827Subproblem 2
x + 16 = -15.066519173 Simplifying x + 16 = -15.066519173 Reorder the terms: 16 + x = -15.066519173 Solving 16 + x = -15.066519173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -15.066519173 + -16 Combine like terms: 16 + -16 = 0 0 + x = -15.066519173 + -16 x = -15.066519173 + -16 Combine like terms: -15.066519173 + -16 = -31.066519173 x = -31.066519173 Simplifying x = -31.066519173Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.933480827, -31.066519173}
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