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Simplifying x = x2 + -78x + 2500 Reorder the terms: x = 2500 + -78x + x2 Solving x = 2500 + -78x + x2 Solving for variable 'x'. Reorder the terms: -2500 + x + 78x + -1x2 = 2500 + -78x + x2 + -2500 + 78x + -1x2 Combine like terms: x + 78x = 79x -2500 + 79x + -1x2 = 2500 + -78x + x2 + -2500 + 78x + -1x2 Reorder the terms: -2500 + 79x + -1x2 = 2500 + -2500 + -78x + 78x + x2 + -1x2 Combine like terms: 2500 + -2500 = 0 -2500 + 79x + -1x2 = 0 + -78x + 78x + x2 + -1x2 -2500 + 79x + -1x2 = -78x + 78x + x2 + -1x2 Combine like terms: -78x + 78x = 0 -2500 + 79x + -1x2 = 0 + x2 + -1x2 -2500 + 79x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2500 + 79x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2500 + -79x + x2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -79x + -2500 + x2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -79x + x2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -79x + x2 = 0 + -2500 -79x + x2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -79x + x2 = -2500 The x term is -79x. Take half its coefficient (-39.5). Square it (1560.25) and add it to both sides. Add '1560.25' to each side of the equation. -79x + 1560.25 + x2 = -2500 + 1560.25 Reorder the terms: 1560.25 + -79x + x2 = -2500 + 1560.25 Combine like terms: -2500 + 1560.25 = -939.75 1560.25 + -79x + x2 = -939.75 Factor a perfect square on the left side: (x + -39.5)(x + -39.5) = -939.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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