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Simplifying 3.2X2 + 8X + 0.8 = 0 Reorder the terms: 0.8 + 8X + 3.2X2 = 0 Solving 0.8 + 8X + 3.2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. 0.25 + 2.5X + X2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 2.5X + -0.25 + X2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 2.5X + X2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 2.5X + X2 = 0 + -0.25 2.5X + X2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 2.5X + X2 = -0.25 The X term is 2.5X. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5X + 1.5625 + X2 = -0.25 + 1.5625 Reorder the terms: 1.5625 + 2.5X + X2 = -0.25 + 1.5625 Combine like terms: -0.25 + 1.5625 = 1.3125 1.5625 + 2.5X + X2 = 1.3125 Factor a perfect square on the left side: (X + 1.25)(X + 1.25) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (X + 1.25) equal to 1.145643924 and -1.145643924.Subproblem 1
X + 1.25 = 1.145643924 Simplifying X + 1.25 = 1.145643924 Reorder the terms: 1.25 + X = 1.145643924 Solving 1.25 + X = 1.145643924 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = 1.145643924 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = 1.145643924 + -1.25 X = 1.145643924 + -1.25 Combine like terms: 1.145643924 + -1.25 = -0.104356076 X = -0.104356076 Simplifying X = -0.104356076Subproblem 2
X + 1.25 = -1.145643924 Simplifying X + 1.25 = -1.145643924 Reorder the terms: 1.25 + X = -1.145643924 Solving 1.25 + X = -1.145643924 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = -1.145643924 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = -1.145643924 + -1.25 X = -1.145643924 + -1.25 Combine like terms: -1.145643924 + -1.25 = -2.395643924 X = -2.395643924 Simplifying X = -2.395643924Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.104356076, -2.395643924}
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