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Simplifying 4X2 + 2.2X + -1.617 = 0 Reorder the terms: -1.617 + 2.2X + 4X2 = 0 Solving -1.617 + 2.2X + 4X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.40425 + 0.55X + X2 = 0 Move the constant term to the right: Add '0.40425' to each side of the equation. -0.40425 + 0.55X + 0.40425 + X2 = 0 + 0.40425 Reorder the terms: -0.40425 + 0.40425 + 0.55X + X2 = 0 + 0.40425 Combine like terms: -0.40425 + 0.40425 = 0.00000 0.00000 + 0.55X + X2 = 0 + 0.40425 0.55X + X2 = 0 + 0.40425 Combine like terms: 0 + 0.40425 = 0.40425 0.55X + X2 = 0.40425 The X term is 0.55X. Take half its coefficient (0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. 0.55X + 0.075625 + X2 = 0.40425 + 0.075625 Reorder the terms: 0.075625 + 0.55X + X2 = 0.40425 + 0.075625 Combine like terms: 0.40425 + 0.075625 = 0.479875 0.075625 + 0.55X + X2 = 0.479875 Factor a perfect square on the left side: (X + 0.275)(X + 0.275) = 0.479875 Calculate the square root of the right side: 0.692730106 Break this problem into two subproblems by setting (X + 0.275) equal to 0.692730106 and -0.692730106.Subproblem 1
X + 0.275 = 0.692730106 Simplifying X + 0.275 = 0.692730106 Reorder the terms: 0.275 + X = 0.692730106 Solving 0.275 + X = 0.692730106 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + X = 0.692730106 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + X = 0.692730106 + -0.275 X = 0.692730106 + -0.275 Combine like terms: 0.692730106 + -0.275 = 0.417730106 X = 0.417730106 Simplifying X = 0.417730106Subproblem 2
X + 0.275 = -0.692730106 Simplifying X + 0.275 = -0.692730106 Reorder the terms: 0.275 + X = -0.692730106 Solving 0.275 + X = -0.692730106 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + X = -0.692730106 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + X = -0.692730106 + -0.275 X = -0.692730106 + -0.275 Combine like terms: -0.692730106 + -0.275 = -0.967730106 X = -0.967730106 Simplifying X = -0.967730106Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.417730106, -0.967730106}
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