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Simplifying 3x * 2x + 20 * 4x + -20 = x Reorder the terms for easier multiplication: 3 * 2x * x + 20 * 4x + -20 = x Multiply 3 * 2 6x * x + 20 * 4x + -20 = x Multiply x * x 6x2 + 20 * 4x + -20 = x Multiply 20 * 4 6x2 + 80x + -20 = x Reorder the terms: -20 + 80x + 6x2 = x Solving -20 + 80x + 6x2 = x Solving for variable 'x'. Reorder the terms: -20 + 80x + -1x + 6x2 = x + -1x Combine like terms: 80x + -1x = 79x -20 + 79x + 6x2 = x + -1x Combine like terms: x + -1x = 0 -20 + 79x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.333333333 + 13.16666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 13.16666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 13.16666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 13.16666667x + x2 = 0 + 3.333333333 13.16666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 13.16666667x + x2 = 3.333333333 The x term is 13.16666667x. Take half its coefficient (6.583333335). Square it (43.34027780) and add it to both sides. Add '43.34027780' to each side of the equation. 13.16666667x + 43.34027780 + x2 = 3.333333333 + 43.34027780 Reorder the terms: 43.34027780 + 13.16666667x + x2 = 3.333333333 + 43.34027780 Combine like terms: 3.333333333 + 43.34027780 = 46.673611133 43.34027780 + 13.16666667x + x2 = 46.673611133 Factor a perfect square on the left side: (x + 6.583333335)(x + 6.583333335) = 46.673611133 Calculate the square root of the right side: 6.831808775 Break this problem into two subproblems by setting (x + 6.583333335) equal to 6.831808775 and -6.831808775.Subproblem 1
x + 6.583333335 = 6.831808775 Simplifying x + 6.583333335 = 6.831808775 Reorder the terms: 6.583333335 + x = 6.831808775 Solving 6.583333335 + x = 6.831808775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.583333335' to each side of the equation. 6.583333335 + -6.583333335 + x = 6.831808775 + -6.583333335 Combine like terms: 6.583333335 + -6.583333335 = 0.000000000 0.000000000 + x = 6.831808775 + -6.583333335 x = 6.831808775 + -6.583333335 Combine like terms: 6.831808775 + -6.583333335 = 0.24847544 x = 0.24847544 Simplifying x = 0.24847544Subproblem 2
x + 6.583333335 = -6.831808775 Simplifying x + 6.583333335 = -6.831808775 Reorder the terms: 6.583333335 + x = -6.831808775 Solving 6.583333335 + x = -6.831808775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.583333335' to each side of the equation. 6.583333335 + -6.583333335 + x = -6.831808775 + -6.583333335 Combine like terms: 6.583333335 + -6.583333335 = 0.000000000 0.000000000 + x = -6.831808775 + -6.583333335 x = -6.831808775 + -6.583333335 Combine like terms: -6.831808775 + -6.583333335 = -13.41514211 x = -13.41514211 Simplifying x = -13.41514211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.24847544, -13.41514211}
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