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Simplifying 16x + 4x2 + -21600 = 0 Reorder the terms: -21600 + 16x + 4x2 = 0 Solving -21600 + 16x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5400 + 4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5400 + 4x + x2)' equal to zero and attempt to solve: Simplifying -5400 + 4x + x2 = 0 Solving -5400 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5400' to each side of the equation. -5400 + 4x + 5400 + x2 = 0 + 5400 Reorder the terms: -5400 + 5400 + 4x + x2 = 0 + 5400 Combine like terms: -5400 + 5400 = 0 0 + 4x + x2 = 0 + 5400 4x + x2 = 0 + 5400 Combine like terms: 0 + 5400 = 5400 4x + x2 = 5400 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 5400 + 4 Reorder the terms: 4 + 4x + x2 = 5400 + 4 Combine like terms: 5400 + 4 = 5404 4 + 4x + x2 = 5404 Factor a perfect square on the left side: (x + 2)(x + 2) = 5404 Calculate the square root of the right side: 73.511903798 Break this problem into two subproblems by setting (x + 2) equal to 73.511903798 and -73.511903798.Subproblem 1
x + 2 = 73.511903798 Simplifying x + 2 = 73.511903798 Reorder the terms: 2 + x = 73.511903798 Solving 2 + x = 73.511903798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 73.511903798 + -2 Combine like terms: 2 + -2 = 0 0 + x = 73.511903798 + -2 x = 73.511903798 + -2 Combine like terms: 73.511903798 + -2 = 71.511903798 x = 71.511903798 Simplifying x = 71.511903798Subproblem 2
x + 2 = -73.511903798 Simplifying x + 2 = -73.511903798 Reorder the terms: 2 + x = -73.511903798 Solving 2 + x = -73.511903798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -73.511903798 + -2 Combine like terms: 2 + -2 = 0 0 + x = -73.511903798 + -2 x = -73.511903798 + -2 Combine like terms: -73.511903798 + -2 = -75.511903798 x = -75.511903798 Simplifying x = -75.511903798Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.511903798, -75.511903798}Solution
x = {71.511903798, -75.511903798}
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