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Simplifying x2 + 0.84x + -0.8 = 0 Reorder the terms: -0.8 + 0.84x + x2 = 0 Solving -0.8 + 0.84x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.84x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.84x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.84x + x2 = 0 + 0.8 0.84x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.84x + x2 = 0.8 The x term is 0.84x. Take half its coefficient (0.42). Square it (0.1764) and add it to both sides. Add '0.1764' to each side of the equation. 0.84x + 0.1764 + x2 = 0.8 + 0.1764 Reorder the terms: 0.1764 + 0.84x + x2 = 0.8 + 0.1764 Combine like terms: 0.8 + 0.1764 = 0.9764 0.1764 + 0.84x + x2 = 0.9764 Factor a perfect square on the left side: (x + 0.42)(x + 0.42) = 0.9764 Calculate the square root of the right side: 0.988129546 Break this problem into two subproblems by setting (x + 0.42) equal to 0.988129546 and -0.988129546.Subproblem 1
x + 0.42 = 0.988129546 Simplifying x + 0.42 = 0.988129546 Reorder the terms: 0.42 + x = 0.988129546 Solving 0.42 + x = 0.988129546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.42' to each side of the equation. 0.42 + -0.42 + x = 0.988129546 + -0.42 Combine like terms: 0.42 + -0.42 = 0.00 0.00 + x = 0.988129546 + -0.42 x = 0.988129546 + -0.42 Combine like terms: 0.988129546 + -0.42 = 0.568129546 x = 0.568129546 Simplifying x = 0.568129546Subproblem 2
x + 0.42 = -0.988129546 Simplifying x + 0.42 = -0.988129546 Reorder the terms: 0.42 + x = -0.988129546 Solving 0.42 + x = -0.988129546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.42' to each side of the equation. 0.42 + -0.42 + x = -0.988129546 + -0.42 Combine like terms: 0.42 + -0.42 = 0.00 0.00 + x = -0.988129546 + -0.42 x = -0.988129546 + -0.42 Combine like terms: -0.988129546 + -0.42 = -1.408129546 x = -1.408129546 Simplifying x = -1.408129546Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.568129546, -1.408129546}
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