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Simplifying x2 + 3.1x + -1.55 = 0 Reorder the terms: -1.55 + 3.1x + x2 = 0 Solving -1.55 + 3.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.55' to each side of the equation. -1.55 + 3.1x + 1.55 + x2 = 0 + 1.55 Reorder the terms: -1.55 + 1.55 + 3.1x + x2 = 0 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + 3.1x + x2 = 0 + 1.55 3.1x + x2 = 0 + 1.55 Combine like terms: 0 + 1.55 = 1.55 3.1x + x2 = 1.55 The x term is 3.1x. Take half its coefficient (1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. 3.1x + 2.4025 + x2 = 1.55 + 2.4025 Reorder the terms: 2.4025 + 3.1x + x2 = 1.55 + 2.4025 Combine like terms: 1.55 + 2.4025 = 3.9525 2.4025 + 3.1x + x2 = 3.9525 Factor a perfect square on the left side: (x + 1.55)(x + 1.55) = 3.9525 Calculate the square root of the right side: 1.988089535 Break this problem into two subproblems by setting (x + 1.55) equal to 1.988089535 and -1.988089535.Subproblem 1
x + 1.55 = 1.988089535 Simplifying x + 1.55 = 1.988089535 Reorder the terms: 1.55 + x = 1.988089535 Solving 1.55 + x = 1.988089535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.55' to each side of the equation. 1.55 + -1.55 + x = 1.988089535 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = 1.988089535 + -1.55 x = 1.988089535 + -1.55 Combine like terms: 1.988089535 + -1.55 = 0.438089535 x = 0.438089535 Simplifying x = 0.438089535Subproblem 2
x + 1.55 = -1.988089535 Simplifying x + 1.55 = -1.988089535 Reorder the terms: 1.55 + x = -1.988089535 Solving 1.55 + x = -1.988089535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.55' to each side of the equation. 1.55 + -1.55 + x = -1.988089535 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = -1.988089535 + -1.55 x = -1.988089535 + -1.55 Combine like terms: -1.988089535 + -1.55 = -3.538089535 x = -3.538089535 Simplifying x = -3.538089535Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.438089535, -3.538089535}
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