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Simplifying x4 + 36x3 + -648x2 = 0 Reorder the terms: -648x2 + 36x3 + x4 = 0 Solving -648x2 + 36x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-648 + 36x + x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-648 + 36x + x2)' equal to zero and attempt to solve: Simplifying -648 + 36x + x2 = 0 Solving -648 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '648' to each side of the equation. -648 + 36x + 648 + x2 = 0 + 648 Reorder the terms: -648 + 648 + 36x + x2 = 0 + 648 Combine like terms: -648 + 648 = 0 0 + 36x + x2 = 0 + 648 36x + x2 = 0 + 648 Combine like terms: 0 + 648 = 648 36x + x2 = 648 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = 648 + 324 Reorder the terms: 324 + 36x + x2 = 648 + 324 Combine like terms: 648 + 324 = 972 324 + 36x + x2 = 972 Factor a perfect square on the left side: (x + 18)(x + 18) = 972 Calculate the square root of the right side: 31.176914536 Break this problem into two subproblems by setting (x + 18) equal to 31.176914536 and -31.176914536.Subproblem 1
x + 18 = 31.176914536 Simplifying x + 18 = 31.176914536 Reorder the terms: 18 + x = 31.176914536 Solving 18 + x = 31.176914536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 31.176914536 + -18 Combine like terms: 18 + -18 = 0 0 + x = 31.176914536 + -18 x = 31.176914536 + -18 Combine like terms: 31.176914536 + -18 = 13.176914536 x = 13.176914536 Simplifying x = 13.176914536Subproblem 2
x + 18 = -31.176914536 Simplifying x + 18 = -31.176914536 Reorder the terms: 18 + x = -31.176914536 Solving 18 + x = -31.176914536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -31.176914536 + -18 Combine like terms: 18 + -18 = 0 0 + x = -31.176914536 + -18 x = -31.176914536 + -18 Combine like terms: -31.176914536 + -18 = -49.176914536 x = -49.176914536 Simplifying x = -49.176914536Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.176914536, -49.176914536}Solution
x = {0, 13.176914536, -49.176914536}
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