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Simplifying 45000x2 + 12740x + -15730 = 0 Reorder the terms: -15730 + 12740x + 45000x2 = 0 Solving -15730 + 12740x + 45000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-1573 + 1274x + 4500x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-1573 + 1274x + 4500x2)' equal to zero and attempt to solve: Simplifying -1573 + 1274x + 4500x2 = 0 Solving -1573 + 1274x + 4500x2 = 0 Begin completing the square. Divide all terms by 4500 the coefficient of the squared term: Divide each side by '4500'. -0.3495555556 + 0.2831111111x + x2 = 0.00 Move the constant term to the right: Add '0.3495555556' to each side of the equation. -0.3495555556 + 0.2831111111x + 0.3495555556 + x2 = 0.00 + 0.3495555556 Reorder the terms: -0.3495555556 + 0.3495555556 + 0.2831111111x + x2 = 0.00 + 0.3495555556 Combine like terms: -0.3495555556 + 0.3495555556 = 0.0000000000 0.0000000000 + 0.2831111111x + x2 = 0.00 + 0.3495555556 0.2831111111x + x2 = 0.00 + 0.3495555556 Combine like terms: 0.00 + 0.3495555556 = 0.3495555556 0.2831111111x + x2 = 0.3495555556 The x term is 0.2831111111x. Take half its coefficient (0.1415555556). Square it (0.02003797532) and add it to both sides. Add '0.02003797532' to each side of the equation. 0.2831111111x + 0.02003797532 + x2 = 0.3495555556 + 0.02003797532 Reorder the terms: 0.02003797532 + 0.2831111111x + x2 = 0.3495555556 + 0.02003797532 Combine like terms: 0.3495555556 + 0.02003797532 = 0.36959353092 0.02003797532 + 0.2831111111x + x2 = 0.36959353092 Factor a perfect square on the left side: (x + 0.1415555556)(x + 0.1415555556) = 0.36959353092 Calculate the square root of the right side: 0.607942046 Break this problem into two subproblems by setting (x + 0.1415555556) equal to 0.607942046 and -0.607942046.Subproblem 1
x + 0.1415555556 = 0.607942046 Simplifying x + 0.1415555556 = 0.607942046 Reorder the terms: 0.1415555556 + x = 0.607942046 Solving 0.1415555556 + x = 0.607942046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1415555556' to each side of the equation. 0.1415555556 + -0.1415555556 + x = 0.607942046 + -0.1415555556 Combine like terms: 0.1415555556 + -0.1415555556 = 0.0000000000 0.0000000000 + x = 0.607942046 + -0.1415555556 x = 0.607942046 + -0.1415555556 Combine like terms: 0.607942046 + -0.1415555556 = 0.4663864904 x = 0.4663864904 Simplifying x = 0.4663864904Subproblem 2
x + 0.1415555556 = -0.607942046 Simplifying x + 0.1415555556 = -0.607942046 Reorder the terms: 0.1415555556 + x = -0.607942046 Solving 0.1415555556 + x = -0.607942046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1415555556' to each side of the equation. 0.1415555556 + -0.1415555556 + x = -0.607942046 + -0.1415555556 Combine like terms: 0.1415555556 + -0.1415555556 = 0.0000000000 0.0000000000 + x = -0.607942046 + -0.1415555556 x = -0.607942046 + -0.1415555556 Combine like terms: -0.607942046 + -0.1415555556 = -0.7494976016 x = -0.7494976016 Simplifying x = -0.7494976016Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4663864904, -0.7494976016}Solution
x = {0.4663864904, -0.7494976016}
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