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Simplifying 2 + x2 + 39x + 15 = 0 Reorder the terms: 2 + 15 + 39x + x2 = 0 Combine like terms: 2 + 15 = 17 17 + 39x + x2 = 0 Solving 17 + 39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 39x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 39x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 39x + x2 = 0 + -17 39x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 39x + x2 = -17 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 = -17 + 380.25 Reorder the terms: 380.25 + 39x + x2 = -17 + 380.25 Combine like terms: -17 + 380.25 = 363.25 380.25 + 39x + x2 = 363.25 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 363.25 Calculate the square root of the right side: 19.059118553 Break this problem into two subproblems by setting (x + 19.5) equal to 19.059118553 and -19.059118553.Subproblem 1
x + 19.5 = 19.059118553 Simplifying x + 19.5 = 19.059118553 Reorder the terms: 19.5 + x = 19.059118553 Solving 19.5 + x = 19.059118553 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 = 19.059118553 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 19.059118553 + -19.5 x = 19.059118553 + -19.5 Combine like terms: 19.059118553 + -19.5 = -0.440881447 x = -0.440881447 Simplifying x = -0.440881447Subproblem 2
x + 19.5 = -19.059118553 Simplifying x + 19.5 = -19.059118553 Reorder the terms: 19.5 + x = -19.059118553 Solving 19.5 + x = -19.059118553 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 = -19.059118553 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -19.059118553 + -19.5 x = -19.059118553 + -19.5 Combine like terms: -19.059118553 + -19.5 = -38.559118553 x = -38.559118553 Simplifying x = -38.559118553Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.440881447, -38.559118553}
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