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Simplifying 6x2 + 30x + 1 = 0 Reorder the terms: 1 + 30x + 6x2 = 0 Solving 1 + 30x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 5x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 5x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 5x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 5x + x2 = 0 + -0.1666666667 5x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 5x + x2 = -0.1666666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -0.1666666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -0.1666666667 + 6.25 Combine like terms: -0.1666666667 + 6.25 = 6.0833333333 6.25 + 5x + x2 = 6.0833333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.0833333333 Calculate the square root of the right side: 2.466441431 Break this problem into two subproblems by setting (x + 2.5) equal to 2.466441431 and -2.466441431.Subproblem 1
x + 2.5 = 2.466441431 Simplifying x + 2.5 = 2.466441431 Reorder the terms: 2.5 + x = 2.466441431 Solving 2.5 + x = 2.466441431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.466441431 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.466441431 + -2.5 x = 2.466441431 + -2.5 Combine like terms: 2.466441431 + -2.5 = -0.033558569 x = -0.033558569 Simplifying x = -0.033558569Subproblem 2
x + 2.5 = -2.466441431 Simplifying x + 2.5 = -2.466441431 Reorder the terms: 2.5 + x = -2.466441431 Solving 2.5 + x = -2.466441431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.466441431 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.466441431 + -2.5 x = -2.466441431 + -2.5 Combine like terms: -2.466441431 + -2.5 = -4.966441431 x = -4.966441431 Simplifying x = -4.966441431Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.033558569, -4.966441431}
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