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Simplifying 11050x2 + -890000x + 500000 = 0 Reorder the terms: 500000 + -890000x + 11050x2 = 0 Solving 500000 + -890000x + 11050x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '50'. 50(10000 + -17800x + 221x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(10000 + -17800x + 221x2)' equal to zero and attempt to solve: Simplifying 10000 + -17800x + 221x2 = 0 Solving 10000 + -17800x + 221x2 = 0 Begin completing the square. Divide all terms by 221 the coefficient of the squared term: Divide each side by '221'. 45.24886878 + -80.54298643x + x2 = 0 Move the constant term to the right: Add '-45.24886878' to each side of the equation. 45.24886878 + -80.54298643x + -45.24886878 + x2 = 0 + -45.24886878 Reorder the terms: 45.24886878 + -45.24886878 + -80.54298643x + x2 = 0 + -45.24886878 Combine like terms: 45.24886878 + -45.24886878 = 0.00000000 0.00000000 + -80.54298643x + x2 = 0 + -45.24886878 -80.54298643x + x2 = 0 + -45.24886878 Combine like terms: 0 + -45.24886878 = -45.24886878 -80.54298643x + x2 = -45.24886878 The x term is -80.54298643x. Take half its coefficient (-40.27149322). Square it (1621.793166) and add it to both sides. Add '1621.793166' to each side of the equation. -80.54298643x + 1621.793166 + x2 = -45.24886878 + 1621.793166 Reorder the terms: 1621.793166 + -80.54298643x + x2 = -45.24886878 + 1621.793166 Combine like terms: -45.24886878 + 1621.793166 = 1576.54429722 1621.793166 + -80.54298643x + x2 = 1576.54429722 Factor a perfect square on the left side: (x + -40.27149322)(x + -40.27149322) = 1576.54429722 Calculate the square root of the right side: 39.705721215 Break this problem into two subproblems by setting (x + -40.27149322) equal to 39.705721215 and -39.705721215.Subproblem 1
x + -40.27149322 = 39.705721215 Simplifying x + -40.27149322 = 39.705721215 Reorder the terms: -40.27149322 + x = 39.705721215 Solving -40.27149322 + x = 39.705721215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.27149322' to each side of the equation. -40.27149322 + 40.27149322 + x = 39.705721215 + 40.27149322 Combine like terms: -40.27149322 + 40.27149322 = 0.00000000 0.00000000 + x = 39.705721215 + 40.27149322 x = 39.705721215 + 40.27149322 Combine like terms: 39.705721215 + 40.27149322 = 79.977214435 x = 79.977214435 Simplifying x = 79.977214435Subproblem 2
x + -40.27149322 = -39.705721215 Simplifying x + -40.27149322 = -39.705721215 Reorder the terms: -40.27149322 + x = -39.705721215 Solving -40.27149322 + x = -39.705721215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.27149322' to each side of the equation. -40.27149322 + 40.27149322 + x = -39.705721215 + 40.27149322 Combine like terms: -40.27149322 + 40.27149322 = 0.00000000 0.00000000 + x = -39.705721215 + 40.27149322 x = -39.705721215 + 40.27149322 Combine like terms: -39.705721215 + 40.27149322 = 0.565772005 x = 0.565772005 Simplifying x = 0.565772005Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.977214435, 0.565772005}Solution
x = {79.977214435, 0.565772005}
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