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Simplifying 6x2 + -1x + -61 = 0 Reorder the terms: -61 + -1x + 6x2 = 0 Solving -61 + -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'. -10.16666667 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '10.16666667' to each side of the equation. -10.16666667 + -0.1666666667x + 10.16666667 + x2 = 0 + 10.16666667 Reorder the terms: -10.16666667 + 10.16666667 + -0.1666666667x + x2 = 0 + 10.16666667 Combine like terms: -10.16666667 + 10.16666667 = 0.00000000 0.00000000 + -0.1666666667x + x2 = 0 + 10.16666667 -0.1666666667x + x2 = 0 + 10.16666667 Combine like terms: 0 + 10.16666667 = 10.16666667 -0.1666666667x + x2 = 10.16666667 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 = 10.16666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 10.16666667 + 0.006944444447 Combine like terms: 10.16666667 + 0.006944444447 = 10.173611114447 0.006944444447 + -0.1666666667x + x2 = 10.173611114447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 10.173611114447 Calculate the square root of the right side: 3.189609869 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 3.189609869 and -3.189609869.Subproblem 1
x + -0.08333333335 = 3.189609869 Simplifying x + -0.08333333335 = 3.189609869 Reorder the terms: -0.08333333335 + x = 3.189609869 Solving -0.08333333335 + x = 3.189609869 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 = 3.189609869 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 3.189609869 + 0.08333333335 x = 3.189609869 + 0.08333333335 Combine like terms: 3.189609869 + 0.08333333335 = 3.27294320235 x = 3.27294320235 Simplifying x = 3.27294320235Subproblem 2
x + -0.08333333335 = -3.189609869 Simplifying x + -0.08333333335 = -3.189609869 Reorder the terms: -0.08333333335 + x = -3.189609869 Solving -0.08333333335 + x = -3.189609869 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 = -3.189609869 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -3.189609869 + 0.08333333335 x = -3.189609869 + 0.08333333335 Combine like terms: -3.189609869 + 0.08333333335 = -3.10627653565 x = -3.10627653565 Simplifying x = -3.10627653565Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.27294320235, -3.10627653565}
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