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Simplifying 0 = -3x2 + 6x + 220 Reorder the terms: 0 = 220 + 6x + -3x2 Solving 0 = 220 + 6x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -220 = -220 -220 + -6x + 3x2 = 220 + 6x + -3x2 + -220 + -6x + 3x2 Reorder the terms: -220 + -6x + 3x2 = 220 + -220 + 6x + -6x + -3x2 + 3x2 Combine like terms: 220 + -220 = 0 -220 + -6x + 3x2 = 0 + 6x + -6x + -3x2 + 3x2 -220 + -6x + 3x2 = 6x + -6x + -3x2 + 3x2 Combine like terms: 6x + -6x = 0 -220 + -6x + 3x2 = 0 + -3x2 + 3x2 -220 + -6x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -220 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -73.33333333 + -2x + x2 = 0 Move the constant term to the right: Add '73.33333333' to each side of the equation. -73.33333333 + -2x + 73.33333333 + x2 = 0 + 73.33333333 Reorder the terms: -73.33333333 + 73.33333333 + -2x + x2 = 0 + 73.33333333 Combine like terms: -73.33333333 + 73.33333333 = 0.00000000 0.00000000 + -2x + x2 = 0 + 73.33333333 -2x + x2 = 0 + 73.33333333 Combine like terms: 0 + 73.33333333 = 73.33333333 -2x + x2 = 73.33333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 73.33333333 + 1 Reorder the terms: 1 + -2x + x2 = 73.33333333 + 1 Combine like terms: 73.33333333 + 1 = 74.33333333 1 + -2x + x2 = 74.33333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 74.33333333 Calculate the square root of the right side: 8.621678104 Break this problem into two subproblems by setting (x + -1) equal to 8.621678104 and -8.621678104.Subproblem 1
x + -1 = 8.621678104 Simplifying x + -1 = 8.621678104 Reorder the terms: -1 + x = 8.621678104 Solving -1 + x = 8.621678104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 8.621678104 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.621678104 + 1 x = 8.621678104 + 1 Combine like terms: 8.621678104 + 1 = 9.621678104 x = 9.621678104 Simplifying x = 9.621678104Subproblem 2
x + -1 = -8.621678104 Simplifying x + -1 = -8.621678104 Reorder the terms: -1 + x = -8.621678104 Solving -1 + x = -8.621678104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -8.621678104 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.621678104 + 1 x = -8.621678104 + 1 Combine like terms: -8.621678104 + 1 = -7.621678104 x = -7.621678104 Simplifying x = -7.621678104Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.621678104, -7.621678104}
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