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Simplifying 2x2 + -18x + -54 = 0 Reorder the terms: -54 + -18x + 2x2 = 0 Solving -54 + -18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + -9x + x2)' equal to zero and attempt to solve: Simplifying -27 + -9x + x2 = 0 Solving -27 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -9x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -9x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -9x + x2 = 0 + 27 -9x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -9x + x2 = 27 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 27 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 27 + 20.25 Combine like terms: 27 + 20.25 = 47.25 20.25 + -9x + x2 = 47.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + -4.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + -4.5 = 6.873863542 Simplifying x + -4.5 = 6.873863542 Reorder the terms: -4.5 + x = 6.873863542 Solving -4.5 + x = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 6.873863542 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.873863542 + 4.5 x = 6.873863542 + 4.5 Combine like terms: 6.873863542 + 4.5 = 11.373863542 x = 11.373863542 Simplifying x = 11.373863542Subproblem 2
x + -4.5 = -6.873863542 Simplifying x + -4.5 = -6.873863542 Reorder the terms: -4.5 + x = -6.873863542 Solving -4.5 + x = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -6.873863542 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.873863542 + 4.5 x = -6.873863542 + 4.5 Combine like terms: -6.873863542 + 4.5 = -2.373863542 x = -2.373863542 Simplifying x = -2.373863542Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.373863542, -2.373863542}Solution
x = {11.373863542, -2.373863542}
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