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Simplifying x2 + 3.1x = 0.9 Reorder the terms: 3.1x + x2 = 0.9 Solving 3.1x + x2 = 0.9 Solving for variable 'x'. Reorder the terms: -0.9 + 3.1x + x2 = 0.9 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 -0.9 + 3.1x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 3.1x + 0.9 + x2 = 0.0 + 0.9 Reorder the terms: -0.9 + 0.9 + 3.1x + x2 = 0.0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 3.1x + x2 = 0.0 + 0.9 3.1x + x2 = 0.0 + 0.9 Combine like terms: 0.0 + 0.9 = 0.9 3.1x + x2 = 0.9 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 = 0.9 + 2.4025 Reorder the terms: 2.4025 + 3.1x + x2 = 0.9 + 2.4025 Combine like terms: 0.9 + 2.4025 = 3.3025 2.4025 + 3.1x + x2 = 3.3025 Factor a perfect square on the left side: (x + 1.55)(x + 1.55) = 3.3025 Calculate the square root of the right side: 1.817278185 Break this problem into two subproblems by setting (x + 1.55) equal to 1.817278185 and -1.817278185.Subproblem 1
x + 1.55 = 1.817278185 Simplifying x + 1.55 = 1.817278185 Reorder the terms: 1.55 + x = 1.817278185 Solving 1.55 + x = 1.817278185 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 = 1.817278185 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = 1.817278185 + -1.55 x = 1.817278185 + -1.55 Combine like terms: 1.817278185 + -1.55 = 0.267278185 x = 0.267278185 Simplifying x = 0.267278185Subproblem 2
x + 1.55 = -1.817278185 Simplifying x + 1.55 = -1.817278185 Reorder the terms: 1.55 + x = -1.817278185 Solving 1.55 + x = -1.817278185 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 = -1.817278185 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = -1.817278185 + -1.55 x = -1.817278185 + -1.55 Combine like terms: -1.817278185 + -1.55 = -3.367278185 x = -3.367278185 Simplifying x = -3.367278185Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.267278185, -3.367278185}
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