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Simplifying x2 + 2x + 0.49 = 0 Reorder the terms: 0.49 + 2x + x2 = 0 Solving 0.49 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.49' to each side of the equation. 0.49 + 2x + -0.49 + x2 = 0 + -0.49 Reorder the terms: 0.49 + -0.49 + 2x + x2 = 0 + -0.49 Combine like terms: 0.49 + -0.49 = 0.00 0.00 + 2x + x2 = 0 + -0.49 2x + x2 = 0 + -0.49 Combine like terms: 0 + -0.49 = -0.49 2x + x2 = -0.49 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.49 + 1 Reorder the terms: 1 + 2x + x2 = -0.49 + 1 Combine like terms: -0.49 + 1 = 0.51 1 + 2x + x2 = 0.51 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.51 Calculate the square root of the right side: 0.714142843 Break this problem into two subproblems by setting (x + 1) equal to 0.714142843 and -0.714142843.Subproblem 1
x + 1 = 0.714142843 Simplifying x + 1 = 0.714142843 Reorder the terms: 1 + x = 0.714142843 Solving 1 + x = 0.714142843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.714142843 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.714142843 + -1 x = 0.714142843 + -1 Combine like terms: 0.714142843 + -1 = -0.285857157 x = -0.285857157 Simplifying x = -0.285857157Subproblem 2
x + 1 = -0.714142843 Simplifying x + 1 = -0.714142843 Reorder the terms: 1 + x = -0.714142843 Solving 1 + x = -0.714142843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.714142843 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.714142843 + -1 x = -0.714142843 + -1 Combine like terms: -0.714142843 + -1 = -1.714142843 x = -1.714142843 Simplifying x = -1.714142843Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.285857157, -1.714142843}
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