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Simplifying 2y2 + -69y + 13 = 0 Reorder the terms: 13 + -69y + 2y2 = 0 Solving 13 + -69y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -34.5y + y2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -34.5y + -6.5 + y2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -34.5y + y2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -34.5y + y2 = 0 + -6.5 -34.5y + y2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -34.5y + y2 = -6.5 The y term is -34.5y. Take half its coefficient (-17.25). Square it (297.5625) and add it to both sides. Add '297.5625' to each side of the equation. -34.5y + 297.5625 + y2 = -6.5 + 297.5625 Reorder the terms: 297.5625 + -34.5y + y2 = -6.5 + 297.5625 Combine like terms: -6.5 + 297.5625 = 291.0625 297.5625 + -34.5y + y2 = 291.0625 Factor a perfect square on the left side: (y + -17.25)(y + -17.25) = 291.0625 Calculate the square root of the right side: 17.060553918 Break this problem into two subproblems by setting (y + -17.25) equal to 17.060553918 and -17.060553918.Subproblem 1
y + -17.25 = 17.060553918 Simplifying y + -17.25 = 17.060553918 Reorder the terms: -17.25 + y = 17.060553918 Solving -17.25 + y = 17.060553918 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17.25' to each side of the equation. -17.25 + 17.25 + y = 17.060553918 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + y = 17.060553918 + 17.25 y = 17.060553918 + 17.25 Combine like terms: 17.060553918 + 17.25 = 34.310553918 y = 34.310553918 Simplifying y = 34.310553918Subproblem 2
y + -17.25 = -17.060553918 Simplifying y + -17.25 = -17.060553918 Reorder the terms: -17.25 + y = -17.060553918 Solving -17.25 + y = -17.060553918 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17.25' to each side of the equation. -17.25 + 17.25 + y = -17.060553918 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + y = -17.060553918 + 17.25 y = -17.060553918 + 17.25 Combine like terms: -17.060553918 + 17.25 = 0.189446082 y = 0.189446082 Simplifying y = 0.189446082Solution
The solution to the problem is based on the solutions from the subproblems. y = {34.310553918, 0.189446082}
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