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Simplifying x2 + 29x + 3 = 0 Reorder the terms: 3 + 29x + x2 = 0 Solving 3 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 29x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 29x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 29x + x2 = 0 + -3 29x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 29x + x2 = -3 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = -3 + 210.25 Reorder the terms: 210.25 + 29x + x2 = -3 + 210.25 Combine like terms: -3 + 210.25 = 207.25 210.25 + 29x + x2 = 207.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 207.25 Calculate the square root of the right side: 14.396180049 Break this problem into two subproblems by setting (x + 14.5) equal to 14.396180049 and -14.396180049.Subproblem 1
x + 14.5 = 14.396180049 Simplifying x + 14.5 = 14.396180049 Reorder the terms: 14.5 + x = 14.396180049 Solving 14.5 + x = 14.396180049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 14.396180049 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 14.396180049 + -14.5 x = 14.396180049 + -14.5 Combine like terms: 14.396180049 + -14.5 = -0.103819951 x = -0.103819951 Simplifying x = -0.103819951Subproblem 2
x + 14.5 = -14.396180049 Simplifying x + 14.5 = -14.396180049 Reorder the terms: 14.5 + x = -14.396180049 Solving 14.5 + x = -14.396180049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -14.396180049 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -14.396180049 + -14.5 x = -14.396180049 + -14.5 Combine like terms: -14.396180049 + -14.5 = -28.896180049 x = -28.896180049 Simplifying x = -28.896180049Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.103819951, -28.896180049}
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