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Simplifying 0 = 3x2 + -18x + 6 Reorder the terms: 0 = 6 + -18x + 3x2 Solving 0 = 6 + -18x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + 18x + -3x2 = 6 + -18x + 3x2 + -6 + 18x + -3x2 Reorder the terms: -6 + 18x + -3x2 = 6 + -6 + -18x + 18x + 3x2 + -3x2 Combine like terms: 6 + -6 = 0 -6 + 18x + -3x2 = 0 + -18x + 18x + 3x2 + -3x2 -6 + 18x + -3x2 = -18x + 18x + 3x2 + -3x2 Combine like terms: -18x + 18x = 0 -6 + 18x + -3x2 = 0 + 3x2 + -3x2 -6 + 18x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -6 + 18x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 6x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 6x + -1x2 = 0 Solving -2 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -6x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -6x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6x + x2 = 0 + -2 -6x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6x + x2 = -2 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -2 + 9 Reorder the terms: 9 + -6x + x2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6x + x2 = 7 Factor a perfect square on the left side: (x + -3)(x + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -3 = 2.645751311 Simplifying x + -3 = 2.645751311 Reorder the terms: -3 + x = 2.645751311 Solving -3 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.645751311 + 3 x = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 x = 5.645751311 Simplifying x = 5.645751311Subproblem 2
x + -3 = -2.645751311 Simplifying x + -3 = -2.645751311 Reorder the terms: -3 + x = -2.645751311 Solving -3 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.645751311 + 3 x = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 x = 0.354248689 Simplifying x = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.645751311, 0.354248689}Solution
x = {5.645751311, 0.354248689}
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