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Simplifying 6x2 + -18x + -243 = 0 Reorder the terms: -243 + -18x + 6x2 = 0 Solving -243 + -18x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-81 + -6x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-81 + -6x + 2x2)' equal to zero and attempt to solve: Simplifying -81 + -6x + 2x2 = 0 Solving -81 + -6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40.5 + -3x + x2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + -3x + 40.5 + x2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + -3x + x2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + -3x + x2 = 0 + 40.5 -3x + x2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 -3x + x2 = 40.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 40.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 40.5 + 2.25 Combine like terms: 40.5 + 2.25 = 42.75 2.25 + -3x + x2 = 42.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 42.75 Calculate the square root of the right side: 6.538348415 Break this problem into two subproblems by setting (x + -1.5) equal to 6.538348415 and -6.538348415.Subproblem 1
x + -1.5 = 6.538348415 Simplifying x + -1.5 = 6.538348415 Reorder the terms: -1.5 + x = 6.538348415 Solving -1.5 + x = 6.538348415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.538348415 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.538348415 + 1.5 x = 6.538348415 + 1.5 Combine like terms: 6.538348415 + 1.5 = 8.038348415 x = 8.038348415 Simplifying x = 8.038348415Subproblem 2
x + -1.5 = -6.538348415 Simplifying x + -1.5 = -6.538348415 Reorder the terms: -1.5 + x = -6.538348415 Solving -1.5 + x = -6.538348415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.538348415 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.538348415 + 1.5 x = -6.538348415 + 1.5 Combine like terms: -6.538348415 + 1.5 = -5.038348415 x = -5.038348415 Simplifying x = -5.038348415Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.038348415, -5.038348415}Solution
x = {8.038348415, -5.038348415}
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