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Simplifying 16x4 + -3360x2 + 72000 = 0 Reorder the terms: 72000 + -3360x2 + 16x4 = 0 Solving 72000 + -3360x2 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(4500 + -210x2 + x4) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(4500 + -210x2 + x4)' equal to zero and attempt to solve: Simplifying 4500 + -210x2 + x4 = 0 Solving 4500 + -210x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-4500' to each side of the equation. 4500 + -210x2 + -4500 + x4 = 0 + -4500 Reorder the terms: 4500 + -4500 + -210x2 + x4 = 0 + -4500 Combine like terms: 4500 + -4500 = 0 0 + -210x2 + x4 = 0 + -4500 -210x2 + x4 = 0 + -4500 Combine like terms: 0 + -4500 = -4500 -210x2 + x4 = -4500 The x term is -210x2. Take half its coefficient (-105). Square it (11025) and add it to both sides. Add '11025' to each side of the equation. -210x2 + 11025 + x4 = -4500 + 11025 Reorder the terms: 11025 + -210x2 + x4 = -4500 + 11025 Combine like terms: -4500 + 11025 = 6525 11025 + -210x2 + x4 = 6525 Factor a perfect square on the left side: (x2 + -105)(x2 + -105) = 6525 Calculate the square root of the right side: 80.777472107 Break this problem into two subproblems by setting (x2 + -105) equal to 80.777472107 and -80.777472107.Subproblem 1
x2 + -105 = 80.777472107 Simplifying x2 + -105 = 80.777472107 Reorder the terms: -105 + x2 = 80.777472107 Solving -105 + x2 = 80.777472107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + x2 = 80.777472107 + 105 Combine like terms: -105 + 105 = 0 0 + x2 = 80.777472107 + 105 x2 = 80.777472107 + 105 Combine like terms: 80.777472107 + 105 = 185.777472107 x2 = 185.777472107 Simplifying x2 = 185.777472107 Take the square root of each side: x = {-13.630020987, 13.630020987}Subproblem 2
x2 + -105 = -80.777472107 Simplifying x2 + -105 = -80.777472107 Reorder the terms: -105 + x2 = -80.777472107 Solving -105 + x2 = -80.777472107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + x2 = -80.777472107 + 105 Combine like terms: -105 + 105 = 0 0 + x2 = -80.777472107 + 105 x2 = -80.777472107 + 105 Combine like terms: -80.777472107 + 105 = 24.222527893 x2 = 24.222527893 Simplifying x2 = 24.222527893 Take the square root of each side: x = {-4.921638741, 4.921638741}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.630020987, 13.630020987, -4.921638741, 4.921638741}Solution
x = {-13.630020987, 13.630020987, -4.921638741, 4.921638741}
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