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Simplifying 0 = -6x2 + 12000x + -21000000 Reorder the terms: 0 = -21000000 + 12000x + -6x2 Solving 0 = -21000000 + 12000x + -6x2 Solving for variable 'x'. Combine like terms: 0 + 21000000 = 21000000 21000000 + -12000x + 6x2 = -21000000 + 12000x + -6x2 + 21000000 + -12000x + 6x2 Reorder the terms: 21000000 + -12000x + 6x2 = -21000000 + 21000000 + 12000x + -12000x + -6x2 + 6x2 Combine like terms: -21000000 + 21000000 = 0 21000000 + -12000x + 6x2 = 0 + 12000x + -12000x + -6x2 + 6x2 21000000 + -12000x + 6x2 = 12000x + -12000x + -6x2 + 6x2 Combine like terms: 12000x + -12000x = 0 21000000 + -12000x + 6x2 = 0 + -6x2 + 6x2 21000000 + -12000x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 21000000 + -12000x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(3500000 + -2000x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3500000 + -2000x + x2)' equal to zero and attempt to solve: Simplifying 3500000 + -2000x + x2 = 0 Solving 3500000 + -2000x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3500000' to each side of the equation. 3500000 + -2000x + -3500000 + x2 = 0 + -3500000 Reorder the terms: 3500000 + -3500000 + -2000x + x2 = 0 + -3500000 Combine like terms: 3500000 + -3500000 = 0 0 + -2000x + x2 = 0 + -3500000 -2000x + x2 = 0 + -3500000 Combine like terms: 0 + -3500000 = -3500000 -2000x + x2 = -3500000 The x term is -2000x. Take half its coefficient (-1000). Square it (1000000) and add it to both sides. Add '1000000' to each side of the equation. -2000x + 1000000 + x2 = -3500000 + 1000000 Reorder the terms: 1000000 + -2000x + x2 = -3500000 + 1000000 Combine like terms: -3500000 + 1000000 = -2500000 1000000 + -2000x + x2 = -2500000 Factor a perfect square on the left side: (x + -1000)(x + -1000) = -2500000 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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