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Simplifying x2 + 39x + 56 = 0 Reorder the terms: 56 + 39x + x2 = 0 Solving 56 + 39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + 39x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + 39x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + 39x + x2 = 0 + -56 39x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 39x + x2 = -56 The x term is 39x. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39x + 380.25 + x2 = -56 + 380.25 Reorder the terms: 380.25 + 39x + x2 = -56 + 380.25 Combine like terms: -56 + 380.25 = 324.25 380.25 + 39x + x2 = 324.25 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 324.25 Calculate the square root of the right side: 18.006943105 Break this problem into two subproblems by setting (x + 19.5) equal to 18.006943105 and -18.006943105.Subproblem 1
x + 19.5 = 18.006943105 Simplifying x + 19.5 = 18.006943105 Reorder the terms: 19.5 + x = 18.006943105 Solving 19.5 + x = 18.006943105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = 18.006943105 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 18.006943105 + -19.5 x = 18.006943105 + -19.5 Combine like terms: 18.006943105 + -19.5 = -1.493056895 x = -1.493056895 Simplifying x = -1.493056895Subproblem 2
x + 19.5 = -18.006943105 Simplifying x + 19.5 = -18.006943105 Reorder the terms: 19.5 + x = -18.006943105 Solving 19.5 + x = -18.006943105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = -18.006943105 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -18.006943105 + -19.5 x = -18.006943105 + -19.5 Combine like terms: -18.006943105 + -19.5 = -37.506943105 x = -37.506943105 Simplifying x = -37.506943105Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.493056895, -37.506943105}
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