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Simplifying 6x2 + -1x + -60 = 0 Reorder the terms: -60 + -1x + 6x2 = 0 Solving -60 + -1x + 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'. -10 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.1666666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -0.1666666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.1666666667x + x2 = 0 + 10 -0.1666666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.1666666667x + x2 = 10 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 10 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 10 + 0.006944444447 Combine like terms: 10 + 0.006944444447 = 10.006944444447 0.006944444447 + -0.1666666667x + x2 = 10.006944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 10.006944444447 Calculate the square root of the right side: 3.163375483 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 3.163375483 and -3.163375483.Subproblem 1
x + -0.08333333335 = 3.163375483 Simplifying x + -0.08333333335 = 3.163375483 Reorder the terms: -0.08333333335 + x = 3.163375483 Solving -0.08333333335 + x = 3.163375483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 3.163375483 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 3.163375483 + 0.08333333335 x = 3.163375483 + 0.08333333335 Combine like terms: 3.163375483 + 0.08333333335 = 3.24670881635 x = 3.24670881635 Simplifying x = 3.24670881635Subproblem 2
x + -0.08333333335 = -3.163375483 Simplifying x + -0.08333333335 = -3.163375483 Reorder the terms: -0.08333333335 + x = -3.163375483 Solving -0.08333333335 + x = -3.163375483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -3.163375483 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -3.163375483 + 0.08333333335 x = -3.163375483 + 0.08333333335 Combine like terms: -3.163375483 + 0.08333333335 = -3.08004214965 x = -3.08004214965 Simplifying x = -3.08004214965Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.24670881635, -3.08004214965}
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