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Simplifying x2 + -39x + 16 = 0 Reorder the terms: 16 + -39x + x2 = 0 Solving 16 + -39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -39x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -39x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -39x + x2 = 0 + -16 -39x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -39x + x2 = -16 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 = -16 + 380.25 Reorder the terms: 380.25 + -39x + x2 = -16 + 380.25 Combine like terms: -16 + 380.25 = 364.25 380.25 + -39x + x2 = 364.25 Factor a perfect square on the left side: (x + -19.5)(x + -19.5) = 364.25 Calculate the square root of the right side: 19.085334684 Break this problem into two subproblems by setting (x + -19.5) equal to 19.085334684 and -19.085334684.Subproblem 1
x + -19.5 = 19.085334684 Simplifying x + -19.5 = 19.085334684 Reorder the terms: -19.5 + x = 19.085334684 Solving -19.5 + x = 19.085334684 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 = 19.085334684 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 19.085334684 + 19.5 x = 19.085334684 + 19.5 Combine like terms: 19.085334684 + 19.5 = 38.585334684 x = 38.585334684 Simplifying x = 38.585334684Subproblem 2
x + -19.5 = -19.085334684 Simplifying x + -19.5 = -19.085334684 Reorder the terms: -19.5 + x = -19.085334684 Solving -19.5 + x = -19.085334684 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 = -19.085334684 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -19.085334684 + 19.5 x = -19.085334684 + 19.5 Combine like terms: -19.085334684 + 19.5 = 0.414665316 x = 0.414665316 Simplifying x = 0.414665316Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.585334684, 0.414665316}
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