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Simplifying 489x + -0.5x2 = 110980 Solving 489x + -0.5x2 = 110980 Solving for variable 'x'. Reorder the terms: -110980 + 489x + -0.5x2 = 110980 + -110980 Combine like terms: 110980 + -110980 = 0 -110980 + 489x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 221960 + -978x + x2 = 0 Move the constant term to the right: Add '-221960' to each side of the equation. 221960 + -978x + -221960 + x2 = 0 + -221960 Reorder the terms: 221960 + -221960 + -978x + x2 = 0 + -221960 Combine like terms: 221960 + -221960 = 0 0 + -978x + x2 = 0 + -221960 -978x + x2 = 0 + -221960 Combine like terms: 0 + -221960 = -221960 -978x + x2 = -221960 The x term is -978x. Take half its coefficient (-489). Square it (239121) and add it to both sides. Add '239121' to each side of the equation. -978x + 239121 + x2 = -221960 + 239121 Reorder the terms: 239121 + -978x + x2 = -221960 + 239121 Combine like terms: -221960 + 239121 = 17161 239121 + -978x + x2 = 17161 Factor a perfect square on the left side: (x + -489)(x + -489) = 17161 Calculate the square root of the right side: 131 Break this problem into two subproblems by setting (x + -489) equal to 131 and -131.Subproblem 1
x + -489 = 131 Simplifying x + -489 = 131 Reorder the terms: -489 + x = 131 Solving -489 + x = 131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '489' to each side of the equation. -489 + 489 + x = 131 + 489 Combine like terms: -489 + 489 = 0 0 + x = 131 + 489 x = 131 + 489 Combine like terms: 131 + 489 = 620 x = 620 Simplifying x = 620Subproblem 2
x + -489 = -131 Simplifying x + -489 = -131 Reorder the terms: -489 + x = -131 Solving -489 + x = -131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '489' to each side of the equation. -489 + 489 + x = -131 + 489 Combine like terms: -489 + 489 = 0 0 + x = -131 + 489 x = -131 + 489 Combine like terms: -131 + 489 = 358 x = 358 Simplifying x = 358Solution
The solution to the problem is based on the solutions from the subproblems. x = {620, 358}
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