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Simplifying -936000x + 334000x2 + 635000 = 0 Reorder the terms: 635000 + -936000x + 334000x2 = 0 Solving 635000 + -936000x + 334000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '1000'. 1000(635 + -936x + 334x2) = 0 Ignore the factor 1000.Subproblem 1
Set the factor '(635 + -936x + 334x2)' equal to zero and attempt to solve: Simplifying 635 + -936x + 334x2 = 0 Solving 635 + -936x + 334x2 = 0 Begin completing the square. Divide all terms by 334 the coefficient of the squared term: Divide each side by '334'. 1.901197605 + -2.80239521x + x2 = 0 Move the constant term to the right: Add '-1.901197605' to each side of the equation. 1.901197605 + -2.80239521x + -1.901197605 + x2 = 0 + -1.901197605 Reorder the terms: 1.901197605 + -1.901197605 + -2.80239521x + x2 = 0 + -1.901197605 Combine like terms: 1.901197605 + -1.901197605 = 0.000000000 0.000000000 + -2.80239521x + x2 = 0 + -1.901197605 -2.80239521x + x2 = 0 + -1.901197605 Combine like terms: 0 + -1.901197605 = -1.901197605 -2.80239521x + x2 = -1.901197605 The x term is -2.80239521x. Take half its coefficient (-1.401197605). Square it (1.963354728) and add it to both sides. Add '1.963354728' to each side of the equation. -2.80239521x + 1.963354728 + x2 = -1.901197605 + 1.963354728 Reorder the terms: 1.963354728 + -2.80239521x + x2 = -1.901197605 + 1.963354728 Combine like terms: -1.901197605 + 1.963354728 = 0.062157123 1.963354728 + -2.80239521x + x2 = 0.062157123 Factor a perfect square on the left side: (x + -1.401197605)(x + -1.401197605) = 0.062157123 Calculate the square root of the right side: 0.249313303 Break this problem into two subproblems by setting (x + -1.401197605) equal to 0.249313303 and -0.249313303.Subproblem 1
x + -1.401197605 = 0.249313303 Simplifying x + -1.401197605 = 0.249313303 Reorder the terms: -1.401197605 + x = 0.249313303 Solving -1.401197605 + x = 0.249313303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.401197605' to each side of the equation. -1.401197605 + 1.401197605 + x = 0.249313303 + 1.401197605 Combine like terms: -1.401197605 + 1.401197605 = 0.000000000 0.000000000 + x = 0.249313303 + 1.401197605 x = 0.249313303 + 1.401197605 Combine like terms: 0.249313303 + 1.401197605 = 1.650510908 x = 1.650510908 Simplifying x = 1.650510908Subproblem 2
x + -1.401197605 = -0.249313303 Simplifying x + -1.401197605 = -0.249313303 Reorder the terms: -1.401197605 + x = -0.249313303 Solving -1.401197605 + x = -0.249313303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.401197605' to each side of the equation. -1.401197605 + 1.401197605 + x = -0.249313303 + 1.401197605 Combine like terms: -1.401197605 + 1.401197605 = 0.000000000 0.000000000 + x = -0.249313303 + 1.401197605 x = -0.249313303 + 1.401197605 Combine like terms: -0.249313303 + 1.401197605 = 1.151884302 x = 1.151884302 Simplifying x = 1.151884302Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.650510908, 1.151884302}Solution
x = {1.650510908, 1.151884302}
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