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Simplifying x2 + 39x + -8 = 0 Reorder the terms: -8 + 39x + x2 = 0 Solving -8 + 39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 39x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 39x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 39x + x2 = 0 + 8 39x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 39x + x2 = 8 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 = 8 + 380.25 Reorder the terms: 380.25 + 39x + x2 = 8 + 380.25 Combine like terms: 8 + 380.25 = 388.25 380.25 + 39x + x2 = 388.25 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 388.25 Calculate the square root of the right side: 19.704060495 Break this problem into two subproblems by setting (x + 19.5) equal to 19.704060495 and -19.704060495.Subproblem 1
x + 19.5 = 19.704060495 Simplifying x + 19.5 = 19.704060495 Reorder the terms: 19.5 + x = 19.704060495 Solving 19.5 + x = 19.704060495 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 = 19.704060495 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 19.704060495 + -19.5 x = 19.704060495 + -19.5 Combine like terms: 19.704060495 + -19.5 = 0.204060495 x = 0.204060495 Simplifying x = 0.204060495Subproblem 2
x + 19.5 = -19.704060495 Simplifying x + 19.5 = -19.704060495 Reorder the terms: 19.5 + x = -19.704060495 Solving 19.5 + x = -19.704060495 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 = -19.704060495 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -19.704060495 + -19.5 x = -19.704060495 + -19.5 Combine like terms: -19.704060495 + -19.5 = -39.204060495 x = -39.204060495 Simplifying x = -39.204060495Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.204060495, -39.204060495}
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