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Simplifying 3x2 + 6x + -36 = x Reorder the terms: -36 + 6x + 3x2 = x Solving -36 + 6x + 3x2 = x Solving for variable 'x'. Reorder the terms: -36 + 6x + -1x + 3x2 = x + -1x Combine like terms: 6x + -1x = 5x -36 + 5x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -36 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 1.666666667x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 1.666666667x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 1.666666667x + x2 = 0 + 12 1.666666667x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 1.666666667x + x2 = 12 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 12 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 12 + 0.6944444447 Combine like terms: 12 + 0.6944444447 = 12.6944444447 0.6944444447 + 1.666666667x + x2 = 12.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 12.6944444447 Calculate the square root of the right side: 3.562926388 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 3.562926388 and -3.562926388.Subproblem 1
x + 0.8333333335 = 3.562926388 Simplifying x + 0.8333333335 = 3.562926388 Reorder the terms: 0.8333333335 + x = 3.562926388 Solving 0.8333333335 + x = 3.562926388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 3.562926388 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 3.562926388 + -0.8333333335 x = 3.562926388 + -0.8333333335 Combine like terms: 3.562926388 + -0.8333333335 = 2.7295930545 x = 2.7295930545 Simplifying x = 2.7295930545Subproblem 2
x + 0.8333333335 = -3.562926388 Simplifying x + 0.8333333335 = -3.562926388 Reorder the terms: 0.8333333335 + x = -3.562926388 Solving 0.8333333335 + x = -3.562926388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -3.562926388 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -3.562926388 + -0.8333333335 x = -3.562926388 + -0.8333333335 Combine like terms: -3.562926388 + -0.8333333335 = -4.3962597215 x = -4.3962597215 Simplifying x = -4.3962597215Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7295930545, -4.3962597215}
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