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Simplifying x2 + -0.6x + -0.55 = 0 Reorder the terms: -0.55 + -0.6x + x2 = 0 Solving -0.55 + -0.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.55' to each side of the equation. -0.55 + -0.6x + 0.55 + x2 = 0 + 0.55 Reorder the terms: -0.55 + 0.55 + -0.6x + x2 = 0 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + -0.6x + x2 = 0 + 0.55 -0.6x + x2 = 0 + 0.55 Combine like terms: 0 + 0.55 = 0.55 -0.6x + x2 = 0.55 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.55 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.55 + 0.09 Combine like terms: 0.55 + 0.09 = 0.64 0.09 + -0.6x + x2 = 0.64 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.64 Calculate the square root of the right side: 0.8 Break this problem into two subproblems by setting (x + -0.3) equal to 0.8 and -0.8.Subproblem 1
x + -0.3 = 0.8 Simplifying x + -0.3 = 0.8 Reorder the terms: -0.3 + x = 0.8 Solving -0.3 + x = 0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.8 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.8 + 0.3 x = 0.8 + 0.3 Combine like terms: 0.8 + 0.3 = 1.1 x = 1.1 Simplifying x = 1.1Subproblem 2
x + -0.3 = -0.8 Simplifying x + -0.3 = -0.8 Reorder the terms: -0.3 + x = -0.8 Solving -0.3 + x = -0.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.8 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.8 + 0.3 x = -0.8 + 0.3 Combine like terms: -0.8 + 0.3 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1, -0.5}
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