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Simplifying 0 = 4x2 + 1250x + -21520 Reorder the terms: 0 = -21520 + 1250x + 4x2 Solving 0 = -21520 + 1250x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 21520 = 21520 21520 + -1250x + -4x2 = -21520 + 1250x + 4x2 + 21520 + -1250x + -4x2 Reorder the terms: 21520 + -1250x + -4x2 = -21520 + 21520 + 1250x + -1250x + 4x2 + -4x2 Combine like terms: -21520 + 21520 = 0 21520 + -1250x + -4x2 = 0 + 1250x + -1250x + 4x2 + -4x2 21520 + -1250x + -4x2 = 1250x + -1250x + 4x2 + -4x2 Combine like terms: 1250x + -1250x = 0 21520 + -1250x + -4x2 = 0 + 4x2 + -4x2 21520 + -1250x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 21520 + -1250x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10760 + -625x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10760 + -625x + -2x2)' equal to zero and attempt to solve: Simplifying 10760 + -625x + -2x2 = 0 Solving 10760 + -625x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5380 + 312.5x + x2 = 0 Move the constant term to the right: Add '5380' to each side of the equation. -5380 + 312.5x + 5380 + x2 = 0 + 5380 Reorder the terms: -5380 + 5380 + 312.5x + x2 = 0 + 5380 Combine like terms: -5380 + 5380 = 0 0 + 312.5x + x2 = 0 + 5380 312.5x + x2 = 0 + 5380 Combine like terms: 0 + 5380 = 5380 312.5x + x2 = 5380 The x term is 312.5x. Take half its coefficient (156.25). Square it (24414.0625) and add it to both sides. Add '24414.0625' to each side of the equation. 312.5x + 24414.0625 + x2 = 5380 + 24414.0625 Reorder the terms: 24414.0625 + 312.5x + x2 = 5380 + 24414.0625 Combine like terms: 5380 + 24414.0625 = 29794.0625 24414.0625 + 312.5x + x2 = 29794.0625 Factor a perfect square on the left side: (x + 156.25)(x + 156.25) = 29794.0625 Calculate the square root of the right side: 172.609566653 Break this problem into two subproblems by setting (x + 156.25) equal to 172.609566653 and -172.609566653.Subproblem 1
x + 156.25 = 172.609566653 Simplifying x + 156.25 = 172.609566653 Reorder the terms: 156.25 + x = 172.609566653 Solving 156.25 + x = 172.609566653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-156.25' to each side of the equation. 156.25 + -156.25 + x = 172.609566653 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 0.00 + x = 172.609566653 + -156.25 x = 172.609566653 + -156.25 Combine like terms: 172.609566653 + -156.25 = 16.359566653 x = 16.359566653 Simplifying x = 16.359566653Subproblem 2
x + 156.25 = -172.609566653 Simplifying x + 156.25 = -172.609566653 Reorder the terms: 156.25 + x = -172.609566653 Solving 156.25 + x = -172.609566653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-156.25' to each side of the equation. 156.25 + -156.25 + x = -172.609566653 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 0.00 + x = -172.609566653 + -156.25 x = -172.609566653 + -156.25 Combine like terms: -172.609566653 + -156.25 = -328.859566653 x = -328.859566653 Simplifying x = -328.859566653Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.359566653, -328.859566653}Solution
x = {16.359566653, -328.859566653}
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