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Simplifying x2 + 2.5x + 1 = 0 Reorder the terms: 1 + 2.5x + x2 = 0 Solving 1 + 2.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.5x + x2 = 0 + -1 2.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.5x + x2 = -1 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 = -1 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -1 + 1.5625 Combine like terms: -1 + 1.5625 = 0.5625 1.5625 + 2.5x + x2 = 0.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (x + 1.25) equal to 0.75 and -0.75.Subproblem 1
x + 1.25 = 0.75 Simplifying x + 1.25 = 0.75 Reorder the terms: 1.25 + x = 0.75 Solving 1.25 + x = 0.75 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 = 0.75 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 0.75 + -1.25 x = 0.75 + -1.25 Combine like terms: 0.75 + -1.25 = -0.5 x = -0.5 Simplifying x = -0.5Subproblem 2
x + 1.25 = -0.75 Simplifying x + 1.25 = -0.75 Reorder the terms: 1.25 + x = -0.75 Solving 1.25 + x = -0.75 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 = -0.75 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -0.75 + -1.25 x = -0.75 + -1.25 Combine like terms: -0.75 + -1.25 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5, -2}
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