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Simplifying x2 + 1.1x + -1.1 = 0 Reorder the terms: -1.1 + 1.1x + x2 = 0 Solving -1.1 + 1.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + 1.1x + 1.1 + x2 = 0 + 1.1 Reorder the terms: -1.1 + 1.1 + 1.1x + x2 = 0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + 1.1x + x2 = 0 + 1.1 1.1x + x2 = 0 + 1.1 Combine like terms: 0 + 1.1 = 1.1 1.1x + x2 = 1.1 The x term is 1.1x. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1x + 0.3025 + x2 = 1.1 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 1.1 + 0.3025 Combine like terms: 1.1 + 0.3025 = 1.4025 0.3025 + 1.1x + x2 = 1.4025 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 1.4025 Calculate the square root of the right side: 1.184271928 Break this problem into two subproblems by setting (x + 0.55) equal to 1.184271928 and -1.184271928.Subproblem 1
x + 0.55 = 1.184271928 Simplifying x + 0.55 = 1.184271928 Reorder the terms: 0.55 + x = 1.184271928 Solving 0.55 + x = 1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = 1.184271928 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 1.184271928 + -0.55 x = 1.184271928 + -0.55 Combine like terms: 1.184271928 + -0.55 = 0.634271928 x = 0.634271928 Simplifying x = 0.634271928Subproblem 2
x + 0.55 = -1.184271928 Simplifying x + 0.55 = -1.184271928 Reorder the terms: 0.55 + x = -1.184271928 Solving 0.55 + x = -1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = -1.184271928 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -1.184271928 + -0.55 x = -1.184271928 + -0.55 Combine like terms: -1.184271928 + -0.55 = -1.734271928 x = -1.734271928 Simplifying x = -1.734271928Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.634271928, -1.734271928}
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