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Simplifying x2 + 0.605x + -3.267 = 0 Reorder the terms: -3.267 + 0.605x + x2 = 0 Solving -3.267 + 0.605x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3.267' to each side of the equation. -3.267 + 0.605x + 3.267 + x2 = 0 + 3.267 Reorder the terms: -3.267 + 3.267 + 0.605x + x2 = 0 + 3.267 Combine like terms: -3.267 + 3.267 = 0.000 0.000 + 0.605x + x2 = 0 + 3.267 0.605x + x2 = 0 + 3.267 Combine like terms: 0 + 3.267 = 3.267 0.605x + x2 = 3.267 The x term is 0.605x. Take half its coefficient (0.3025). Square it (0.09150625) and add it to both sides. Add '0.09150625' to each side of the equation. 0.605x + 0.09150625 + x2 = 3.267 + 0.09150625 Reorder the terms: 0.09150625 + 0.605x + x2 = 3.267 + 0.09150625 Combine like terms: 3.267 + 0.09150625 = 3.35850625 0.09150625 + 0.605x + x2 = 3.35850625 Factor a perfect square on the left side: (x + 0.3025)(x + 0.3025) = 3.35850625 Calculate the square root of the right side: 1.832622779 Break this problem into two subproblems by setting (x + 0.3025) equal to 1.832622779 and -1.832622779.Subproblem 1
x + 0.3025 = 1.832622779 Simplifying x + 0.3025 = 1.832622779 Reorder the terms: 0.3025 + x = 1.832622779 Solving 0.3025 + x = 1.832622779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3025' to each side of the equation. 0.3025 + -0.3025 + x = 1.832622779 + -0.3025 Combine like terms: 0.3025 + -0.3025 = 0.0000 0.0000 + x = 1.832622779 + -0.3025 x = 1.832622779 + -0.3025 Combine like terms: 1.832622779 + -0.3025 = 1.530122779 x = 1.530122779 Simplifying x = 1.530122779Subproblem 2
x + 0.3025 = -1.832622779 Simplifying x + 0.3025 = -1.832622779 Reorder the terms: 0.3025 + x = -1.832622779 Solving 0.3025 + x = -1.832622779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3025' to each side of the equation. 0.3025 + -0.3025 + x = -1.832622779 + -0.3025 Combine like terms: 0.3025 + -0.3025 = 0.0000 0.0000 + x = -1.832622779 + -0.3025 x = -1.832622779 + -0.3025 Combine like terms: -1.832622779 + -0.3025 = -2.135122779 x = -2.135122779 Simplifying x = -2.135122779Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.530122779, -2.135122779}
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