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Simplifying 18 = 3x(3x + -6) Reorder the terms: 18 = 3x(-6 + 3x) 18 = (-6 * 3x + 3x * 3x) 18 = (-18x + 9x2) Solving 18 = -18x + 9x2 Solving for variable 'x'. Reorder the terms: 18 + 18x + -9x2 = -18x + 18x + 9x2 + -9x2 Combine like terms: -18x + 18x = 0 18 + 18x + -9x2 = 0 + 9x2 + -9x2 18 + 18x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 18 + 18x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(2 + 2x + -1x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(2 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + 2x + -1x2 = 0 Solving 2 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -2x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2x + x2 = 0 + 2 -2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2x + x2 = 2 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 = 2 + 1 Reorder the terms: 1 + -2x + x2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2x + x2 = 3 Factor a perfect square on the left side: (x + -1)(x + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -1 = 1.732050808 Simplifying x + -1 = 1.732050808 Reorder the terms: -1 + x = 1.732050808 Solving -1 + x = 1.732050808 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 = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.732050808 + 1 x = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 x = 2.732050808 Simplifying x = 2.732050808Subproblem 2
x + -1 = -1.732050808 Simplifying x + -1 = -1.732050808 Reorder the terms: -1 + x = -1.732050808 Solving -1 + x = -1.732050808 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 = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.732050808 + 1 x = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 x = -0.732050808 Simplifying x = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.732050808, -0.732050808}Solution
x = {2.732050808, -0.732050808}
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