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Simplifying 36x2 + 324x + -7776 = 0 Reorder the terms: -7776 + 324x + 36x2 = 0 Solving -7776 + 324x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '36'. 36(-216 + 9x + x2) = 0 Ignore the factor 36.Subproblem 1
Set the factor '(-216 + 9x + x2)' equal to zero and attempt to solve: Simplifying -216 + 9x + x2 = 0 Solving -216 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '216' to each side of the equation. -216 + 9x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + 9x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 9x + x2 = 0 + 216 9x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 9x + x2 = 216 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 = 216 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 216 + 20.25 Combine like terms: 216 + 20.25 = 236.25 20.25 + 9x + x2 = 236.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (x + 4.5) equal to 15.370426149 and -15.370426149.Subproblem 1
x + 4.5 = 15.370426149 Simplifying x + 4.5 = 15.370426149 Reorder the terms: 4.5 + x = 15.370426149 Solving 4.5 + x = 15.370426149 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 = 15.370426149 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 15.370426149 + -4.5 x = 15.370426149 + -4.5 Combine like terms: 15.370426149 + -4.5 = 10.870426149 x = 10.870426149 Simplifying x = 10.870426149Subproblem 2
x + 4.5 = -15.370426149 Simplifying x + 4.5 = -15.370426149 Reorder the terms: 4.5 + x = -15.370426149 Solving 4.5 + x = -15.370426149 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 = -15.370426149 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -15.370426149 + -4.5 x = -15.370426149 + -4.5 Combine like terms: -15.370426149 + -4.5 = -19.870426149 x = -19.870426149 Simplifying x = -19.870426149Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.870426149, -19.870426149}Solution
x = {10.870426149, -19.870426149}
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