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Simplifying x2 + 1.1x = 0.6975 Reorder the terms: 1.1x + x2 = 0.6975 Solving 1.1x + x2 = 0.6975 Solving for variable 'x'. Reorder the terms: -0.6975 + 1.1x + x2 = 0.6975 + -0.6975 Combine like terms: 0.6975 + -0.6975 = 0.0000 -0.6975 + 1.1x + x2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '0.6975' to each side of the equation. -0.6975 + 1.1x + 0.6975 + x2 = 0.0000 + 0.6975 Reorder the terms: -0.6975 + 0.6975 + 1.1x + x2 = 0.0000 + 0.6975 Combine like terms: -0.6975 + 0.6975 = 0.0000 0.0000 + 1.1x + x2 = 0.0000 + 0.6975 1.1x + x2 = 0.0000 + 0.6975 Combine like terms: 0.0000 + 0.6975 = 0.6975 1.1x + x2 = 0.6975 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 = 0.6975 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 0.6975 + 0.3025 Combine like terms: 0.6975 + 0.3025 = 1 0.3025 + 1.1x + x2 = 1 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + 0.55) equal to 1 and -1.Subproblem 1
x + 0.55 = 1 Simplifying x + 0.55 = 1 Reorder the terms: 0.55 + x = 1 Solving 0.55 + x = 1 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 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 1 + -0.55 x = 1 + -0.55 Combine like terms: 1 + -0.55 = 0.45 x = 0.45 Simplifying x = 0.45Subproblem 2
x + 0.55 = -1 Simplifying x + 0.55 = -1 Reorder the terms: 0.55 + x = -1 Solving 0.55 + x = -1 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 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -1 + -0.55 x = -1 + -0.55 Combine like terms: -1 + -0.55 = -1.55 x = -1.55 Simplifying x = -1.55Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.45, -1.55}
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