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Simplifying 9y2 + -294y + 1345 = 0 Reorder the terms: 1345 + -294y + 9y2 = 0 Solving 1345 + -294y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 149.4444444 + -32.66666667y + y2 = 0 Move the constant term to the right: Add '-149.4444444' to each side of the equation. 149.4444444 + -32.66666667y + -149.4444444 + y2 = 0 + -149.4444444 Reorder the terms: 149.4444444 + -149.4444444 + -32.66666667y + y2 = 0 + -149.4444444 Combine like terms: 149.4444444 + -149.4444444 = 0.0000000 0.0000000 + -32.66666667y + y2 = 0 + -149.4444444 -32.66666667y + y2 = 0 + -149.4444444 Combine like terms: 0 + -149.4444444 = -149.4444444 -32.66666667y + y2 = -149.4444444 The y term is -32.66666667y. Take half its coefficient (-16.33333334). Square it (266.7777780) and add it to both sides. Add '266.7777780' to each side of the equation. -32.66666667y + 266.7777780 + y2 = -149.4444444 + 266.7777780 Reorder the terms: 266.7777780 + -32.66666667y + y2 = -149.4444444 + 266.7777780 Combine like terms: -149.4444444 + 266.7777780 = 117.3333336 266.7777780 + -32.66666667y + y2 = 117.3333336 Factor a perfect square on the left side: (y + -16.33333334)(y + -16.33333334) = 117.3333336 Calculate the square root of the right side: 10.832051218 Break this problem into two subproblems by setting (y + -16.33333334) equal to 10.832051218 and -10.832051218.Subproblem 1
y + -16.33333334 = 10.832051218 Simplifying y + -16.33333334 = 10.832051218 Reorder the terms: -16.33333334 + y = 10.832051218 Solving -16.33333334 + y = 10.832051218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '16.33333334' to each side of the equation. -16.33333334 + 16.33333334 + y = 10.832051218 + 16.33333334 Combine like terms: -16.33333334 + 16.33333334 = 0.00000000 0.00000000 + y = 10.832051218 + 16.33333334 y = 10.832051218 + 16.33333334 Combine like terms: 10.832051218 + 16.33333334 = 27.165384558 y = 27.165384558 Simplifying y = 27.165384558Subproblem 2
y + -16.33333334 = -10.832051218 Simplifying y + -16.33333334 = -10.832051218 Reorder the terms: -16.33333334 + y = -10.832051218 Solving -16.33333334 + y = -10.832051218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '16.33333334' to each side of the equation. -16.33333334 + 16.33333334 + y = -10.832051218 + 16.33333334 Combine like terms: -16.33333334 + 16.33333334 = 0.00000000 0.00000000 + y = -10.832051218 + 16.33333334 y = -10.832051218 + 16.33333334 Combine like terms: -10.832051218 + 16.33333334 = 5.501282122 y = 5.501282122 Simplifying y = 5.501282122Solution
The solution to the problem is based on the solutions from the subproblems. y = {27.165384558, 5.501282122}
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