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Simplifying x2 + 39x + 5 = 0 Reorder the terms: 5 + 39x + x2 = 0 Solving 5 + 39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 39x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 39x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 39x + x2 = 0 + -5 39x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 39x + x2 = -5 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 = -5 + 380.25 Reorder the terms: 380.25 + 39x + x2 = -5 + 380.25 Combine like terms: -5 + 380.25 = 375.25 380.25 + 39x + x2 = 375.25 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 375.25 Calculate the square root of the right side: 19.371370628 Break this problem into two subproblems by setting (x + 19.5) equal to 19.371370628 and -19.371370628.Subproblem 1
x + 19.5 = 19.371370628 Simplifying x + 19.5 = 19.371370628 Reorder the terms: 19.5 + x = 19.371370628 Solving 19.5 + x = 19.371370628 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 = 19.371370628 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 19.371370628 + -19.5 x = 19.371370628 + -19.5 Combine like terms: 19.371370628 + -19.5 = -0.128629372 x = -0.128629372 Simplifying x = -0.128629372Subproblem 2
x + 19.5 = -19.371370628 Simplifying x + 19.5 = -19.371370628 Reorder the terms: 19.5 + x = -19.371370628 Solving 19.5 + x = -19.371370628 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 = -19.371370628 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -19.371370628 + -19.5 x = -19.371370628 + -19.5 Combine like terms: -19.371370628 + -19.5 = -38.871370628 x = -38.871370628 Simplifying x = -38.871370628Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.128629372, -38.871370628}
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