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Simplifying 5(x2 + -18x + -54) = 0 Reorder the terms: 5(-54 + -18x + x2) = 0 (-54 * 5 + -18x * 5 + x2 * 5) = 0 (-270 + -90x + 5x2) = 0 Solving -270 + -90x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-54 + -18x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-54 + -18x + x2)' equal to zero and attempt to solve: Simplifying -54 + -18x + x2 = 0 Solving -54 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -18x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -18x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -18x + x2 = 0 + 54 -18x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -18x + x2 = 54 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 54 + 81 Reorder the terms: 81 + -18x + x2 = 54 + 81 Combine like terms: 54 + 81 = 135 81 + -18x + x2 = 135 Factor a perfect square on the left side: (x + -9)(x + -9) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (x + -9) equal to 11.618950039 and -11.618950039.Subproblem 1
x + -9 = 11.618950039 Simplifying x + -9 = 11.618950039 Reorder the terms: -9 + x = 11.618950039 Solving -9 + x = 11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 11.618950039 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11.618950039 + 9 x = 11.618950039 + 9 Combine like terms: 11.618950039 + 9 = 20.618950039 x = 20.618950039 Simplifying x = 20.618950039Subproblem 2
x + -9 = -11.618950039 Simplifying x + -9 = -11.618950039 Reorder the terms: -9 + x = -11.618950039 Solving -9 + x = -11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -11.618950039 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11.618950039 + 9 x = -11.618950039 + 9 Combine like terms: -11.618950039 + 9 = -2.618950039 x = -2.618950039 Simplifying x = -2.618950039Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.618950039, -2.618950039}Solution
x = {20.618950039, -2.618950039}
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