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Simplifying 18y + 7y2 = 180 Solving 18y + 7y2 = 180 Solving for variable 'y'. Reorder the terms: -180 + 18y + 7y2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 18y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -25.71428571 + 2.571428571y + y2 = 0 Move the constant term to the right: Add '25.71428571' to each side of the equation. -25.71428571 + 2.571428571y + 25.71428571 + y2 = 0 + 25.71428571 Reorder the terms: -25.71428571 + 25.71428571 + 2.571428571y + y2 = 0 + 25.71428571 Combine like terms: -25.71428571 + 25.71428571 = 0.00000000 0.00000000 + 2.571428571y + y2 = 0 + 25.71428571 2.571428571y + y2 = 0 + 25.71428571 Combine like terms: 0 + 25.71428571 = 25.71428571 2.571428571y + y2 = 25.71428571 The y term is 2.571428571y. Take half its coefficient (1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. 2.571428571y + 1.653061225 + y2 = 25.71428571 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571y + y2 = 25.71428571 + 1.653061225 Combine like terms: 25.71428571 + 1.653061225 = 27.367346935 1.653061225 + 2.571428571y + y2 = 27.367346935 Factor a perfect square on the left side: (y + 1.285714286)(y + 1.285714286) = 27.367346935 Calculate the square root of the right side: 5.231380978 Break this problem into two subproblems by setting (y + 1.285714286) equal to 5.231380978 and -5.231380978.Subproblem 1
y + 1.285714286 = 5.231380978 Simplifying y + 1.285714286 = 5.231380978 Reorder the terms: 1.285714286 + y = 5.231380978 Solving 1.285714286 + y = 5.231380978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + y = 5.231380978 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + y = 5.231380978 + -1.285714286 y = 5.231380978 + -1.285714286 Combine like terms: 5.231380978 + -1.285714286 = 3.945666692 y = 3.945666692 Simplifying y = 3.945666692Subproblem 2
y + 1.285714286 = -5.231380978 Simplifying y + 1.285714286 = -5.231380978 Reorder the terms: 1.285714286 + y = -5.231380978 Solving 1.285714286 + y = -5.231380978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + y = -5.231380978 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + y = -5.231380978 + -1.285714286 y = -5.231380978 + -1.285714286 Combine like terms: -5.231380978 + -1.285714286 = -6.517095264 y = -6.517095264 Simplifying y = -6.517095264Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.945666692, -6.517095264}
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