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Simplifying x2 + 3.81x + 3.61 = 0 Reorder the terms: 3.61 + 3.81x + x2 = 0 Solving 3.61 + 3.81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3.61' to each side of the equation. 3.61 + 3.81x + -3.61 + x2 = 0 + -3.61 Reorder the terms: 3.61 + -3.61 + 3.81x + x2 = 0 + -3.61 Combine like terms: 3.61 + -3.61 = 0.00 0.00 + 3.81x + x2 = 0 + -3.61 3.81x + x2 = 0 + -3.61 Combine like terms: 0 + -3.61 = -3.61 3.81x + x2 = -3.61 The x term is 3.81x. Take half its coefficient (1.905). Square it (3.629025) and add it to both sides. Add '3.629025' to each side of the equation. 3.81x + 3.629025 + x2 = -3.61 + 3.629025 Reorder the terms: 3.629025 + 3.81x + x2 = -3.61 + 3.629025 Combine like terms: -3.61 + 3.629025 = 0.019025 3.629025 + 3.81x + x2 = 0.019025 Factor a perfect square on the left side: (x + 1.905)(x + 1.905) = 0.019025 Calculate the square root of the right side: 0.137931142 Break this problem into two subproblems by setting (x + 1.905) equal to 0.137931142 and -0.137931142.Subproblem 1
x + 1.905 = 0.137931142 Simplifying x + 1.905 = 0.137931142 Reorder the terms: 1.905 + x = 0.137931142 Solving 1.905 + x = 0.137931142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.905' to each side of the equation. 1.905 + -1.905 + x = 0.137931142 + -1.905 Combine like terms: 1.905 + -1.905 = 0.000 0.000 + x = 0.137931142 + -1.905 x = 0.137931142 + -1.905 Combine like terms: 0.137931142 + -1.905 = -1.767068858 x = -1.767068858 Simplifying x = -1.767068858Subproblem 2
x + 1.905 = -0.137931142 Simplifying x + 1.905 = -0.137931142 Reorder the terms: 1.905 + x = -0.137931142 Solving 1.905 + x = -0.137931142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.905' to each side of the equation. 1.905 + -1.905 + x = -0.137931142 + -1.905 Combine like terms: 1.905 + -1.905 = 0.000 0.000 + x = -0.137931142 + -1.905 x = -0.137931142 + -1.905 Combine like terms: -0.137931142 + -1.905 = -2.042931142 x = -2.042931142 Simplifying x = -2.042931142Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.767068858, -2.042931142}
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