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Simplifying 3 = 9x2 + -18x Reorder the terms: 3 = -18x + 9x2 Solving 3 = -18x + 9x2 Solving for variable 'x'. Reorder the terms: 3 + 18x + -9x2 = -18x + 18x + 9x2 + -9x2 Combine like terms: -18x + 18x = 0 3 + 18x + -9x2 = 0 + 9x2 + -9x2 3 + 18x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 3 + 18x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 6x + -3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 6x + -3x2)' equal to zero and attempt to solve: Simplifying 1 + 6x + -3x2 = 0 Solving 1 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.3333333333 + -2x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -2x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -2x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + 0.3333333333 -2x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -2x + x2 = 0.3333333333 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 = 0.3333333333 + 1 Reorder the terms: 1 + -2x + x2 = 0.3333333333 + 1 Combine like terms: 0.3333333333 + 1 = 1.3333333333 1 + -2x + x2 = 1.3333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.3333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (x + -1) equal to 1.154700538 and -1.154700538.Subproblem 1
x + -1 = 1.154700538 Simplifying x + -1 = 1.154700538 Reorder the terms: -1 + x = 1.154700538 Solving -1 + x = 1.154700538 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 = 1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.154700538 + 1 x = 1.154700538 + 1 Combine like terms: 1.154700538 + 1 = 2.154700538 x = 2.154700538 Simplifying x = 2.154700538Subproblem 2
x + -1 = -1.154700538 Simplifying x + -1 = -1.154700538 Reorder the terms: -1 + x = -1.154700538 Solving -1 + x = -1.154700538 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 = -1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.154700538 + 1 x = -1.154700538 + 1 Combine like terms: -1.154700538 + 1 = -0.154700538 x = -0.154700538 Simplifying x = -0.154700538Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.154700538, -0.154700538}Solution
x = {2.154700538, -0.154700538}
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