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Simplifying 68000 = 2x2 + -2000x + 1000000 Reorder the terms: 68000 = 1000000 + -2000x + 2x2 Solving 68000 = 1000000 + -2000x + 2x2 Solving for variable 'x'. Combine like terms: 68000 + -1000000 = -932000 -932000 + 2000x + -2x2 = 1000000 + -2000x + 2x2 + -1000000 + 2000x + -2x2 Reorder the terms: -932000 + 2000x + -2x2 = 1000000 + -1000000 + -2000x + 2000x + 2x2 + -2x2 Combine like terms: 1000000 + -1000000 = 0 -932000 + 2000x + -2x2 = 0 + -2000x + 2000x + 2x2 + -2x2 -932000 + 2000x + -2x2 = -2000x + 2000x + 2x2 + -2x2 Combine like terms: -2000x + 2000x = 0 -932000 + 2000x + -2x2 = 0 + 2x2 + -2x2 -932000 + 2000x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -932000 + 2000x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-466000 + 1000x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-466000 + 1000x + -1x2)' equal to zero and attempt to solve: Simplifying -466000 + 1000x + -1x2 = 0 Solving -466000 + 1000x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 466000 + -1000x + x2 = 0 Move the constant term to the right: Add '-466000' to each side of the equation. 466000 + -1000x + -466000 + x2 = 0 + -466000 Reorder the terms: 466000 + -466000 + -1000x + x2 = 0 + -466000 Combine like terms: 466000 + -466000 = 0 0 + -1000x + x2 = 0 + -466000 -1000x + x2 = 0 + -466000 Combine like terms: 0 + -466000 = -466000 -1000x + x2 = -466000 The x term is -1000x. Take half its coefficient (-500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. -1000x + 250000 + x2 = -466000 + 250000 Reorder the terms: 250000 + -1000x + x2 = -466000 + 250000 Combine like terms: -466000 + 250000 = -216000 250000 + -1000x + x2 = -216000 Factor a perfect square on the left side: (x + -500)(x + -500) = -216000 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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