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Simplifying 7.29y2 + -3080y + 100170 = 0 Reorder the terms: 100170 + -3080y + 7.29y2 = 0 Solving 100170 + -3080y + 7.29y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7.29 the coefficient of the squared term: Divide each side by '7.29'. 13740.74074 + -422.4965706y + y2 = 0 Move the constant term to the right: Add '-13740.74074' to each side of the equation. 13740.74074 + -422.4965706y + -13740.74074 + y2 = 0 + -13740.74074 Reorder the terms: 13740.74074 + -13740.74074 + -422.4965706y + y2 = 0 + -13740.74074 Combine like terms: 13740.74074 + -13740.74074 = 0.00000 0.00000 + -422.4965706y + y2 = 0 + -13740.74074 -422.4965706y + y2 = 0 + -13740.74074 Combine like terms: 0 + -13740.74074 = -13740.74074 -422.4965706y + y2 = -13740.74074 The y term is -422.4965706y. Take half its coefficient (-211.2482853). Square it (44625.83804) and add it to both sides. Add '44625.83804' to each side of the equation. -422.4965706y + 44625.83804 + y2 = -13740.74074 + 44625.83804 Reorder the terms: 44625.83804 + -422.4965706y + y2 = -13740.74074 + 44625.83804 Combine like terms: -13740.74074 + 44625.83804 = 30885.0973 44625.83804 + -422.4965706y + y2 = 30885.0973 Factor a perfect square on the left side: (y + -211.2482853)(y + -211.2482853) = 30885.0973 Calculate the square root of the right side: 175.741563951 Break this problem into two subproblems by setting (y + -211.2482853) equal to 175.741563951 and -175.741563951.Subproblem 1
y + -211.2482853 = 175.741563951 Simplifying y + -211.2482853 = 175.741563951 Reorder the terms: -211.2482853 + y = 175.741563951 Solving -211.2482853 + y = 175.741563951 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '211.2482853' to each side of the equation. -211.2482853 + 211.2482853 + y = 175.741563951 + 211.2482853 Combine like terms: -211.2482853 + 211.2482853 = 0.0000000 0.0000000 + y = 175.741563951 + 211.2482853 y = 175.741563951 + 211.2482853 Combine like terms: 175.741563951 + 211.2482853 = 386.989849251 y = 386.989849251 Simplifying y = 386.989849251Subproblem 2
y + -211.2482853 = -175.741563951 Simplifying y + -211.2482853 = -175.741563951 Reorder the terms: -211.2482853 + y = -175.741563951 Solving -211.2482853 + y = -175.741563951 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '211.2482853' to each side of the equation. -211.2482853 + 211.2482853 + y = -175.741563951 + 211.2482853 Combine like terms: -211.2482853 + 211.2482853 = 0.0000000 0.0000000 + y = -175.741563951 + 211.2482853 y = -175.741563951 + 211.2482853 Combine like terms: -175.741563951 + 211.2482853 = 35.506721349 y = 35.506721349 Simplifying y = 35.506721349Solution
The solution to the problem is based on the solutions from the subproblems. y = {386.989849251, 35.506721349}
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