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Simplifying 0 = 4x2 + -1600x + 174000 Reorder the terms: 0 = 174000 + -1600x + 4x2 Solving 0 = 174000 + -1600x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -174000 = -174000 -174000 + 1600x + -4x2 = 174000 + -1600x + 4x2 + -174000 + 1600x + -4x2 Reorder the terms: -174000 + 1600x + -4x2 = 174000 + -174000 + -1600x + 1600x + 4x2 + -4x2 Combine like terms: 174000 + -174000 = 0 -174000 + 1600x + -4x2 = 0 + -1600x + 1600x + 4x2 + -4x2 -174000 + 1600x + -4x2 = -1600x + 1600x + 4x2 + -4x2 Combine like terms: -1600x + 1600x = 0 -174000 + 1600x + -4x2 = 0 + 4x2 + -4x2 -174000 + 1600x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -174000 + 1600x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-43500 + 400x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-43500 + 400x + -1x2)' equal to zero and attempt to solve: Simplifying -43500 + 400x + -1x2 = 0 Solving -43500 + 400x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 43500 + -400x + x2 = 0 Move the constant term to the right: Add '-43500' to each side of the equation. 43500 + -400x + -43500 + x2 = 0 + -43500 Reorder the terms: 43500 + -43500 + -400x + x2 = 0 + -43500 Combine like terms: 43500 + -43500 = 0 0 + -400x + x2 = 0 + -43500 -400x + x2 = 0 + -43500 Combine like terms: 0 + -43500 = -43500 -400x + x2 = -43500 The x term is -400x. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400x + 40000 + x2 = -43500 + 40000 Reorder the terms: 40000 + -400x + x2 = -43500 + 40000 Combine like terms: -43500 + 40000 = -3500 40000 + -400x + x2 = -3500 Factor a perfect square on the left side: (x + -200)(x + -200) = -3500 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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