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Simplifying 100x + -1x2 = 5000 Solving 100x + -1x2 = 5000 Solving for variable 'x'. Reorder the terms: -5000 + 100x + -1x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -5000 + 100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5000 + -100x + x2 = 0 Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -100x + -5000 + x2 = 0 + -5000 Reorder the terms: 5000 + -5000 + -100x + x2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -100x + x2 = 0 + -5000 -100x + x2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -100x + x2 = -5000 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -5000 + 2500 Reorder the terms: 2500 + -100x + x2 = -5000 + 2500 Combine like terms: -5000 + 2500 = -2500 2500 + -100x + x2 = -2500 Factor a perfect square on the left side: (x + -50)(x + -50) = -2500 Can't calculate square root of the right side. The solution to this equation could not be determined.
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