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Simplifying 14y2 + 58y + 15 = 0 Reorder the terms: 15 + 58y + 14y2 = 0 Solving 15 + 58y + 14y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 1.071428571 + 4.142857143y + y2 = 0 Move the constant term to the right: Add '-1.071428571' to each side of the equation. 1.071428571 + 4.142857143y + -1.071428571 + y2 = 0 + -1.071428571 Reorder the terms: 1.071428571 + -1.071428571 + 4.142857143y + y2 = 0 + -1.071428571 Combine like terms: 1.071428571 + -1.071428571 = 0.000000000 0.000000000 + 4.142857143y + y2 = 0 + -1.071428571 4.142857143y + y2 = 0 + -1.071428571 Combine like terms: 0 + -1.071428571 = -1.071428571 4.142857143y + y2 = -1.071428571 The y term is 4.142857143y. Take half its coefficient (2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. 4.142857143y + 4.290816329 + y2 = -1.071428571 + 4.290816329 Reorder the terms: 4.290816329 + 4.142857143y + y2 = -1.071428571 + 4.290816329 Combine like terms: -1.071428571 + 4.290816329 = 3.219387758 4.290816329 + 4.142857143y + y2 = 3.219387758 Factor a perfect square on the left side: (y + 2.071428572)(y + 2.071428572) = 3.219387758 Calculate the square root of the right side: 1.794265242 Break this problem into two subproblems by setting (y + 2.071428572) equal to 1.794265242 and -1.794265242.Subproblem 1
y + 2.071428572 = 1.794265242 Simplifying y + 2.071428572 = 1.794265242 Reorder the terms: 2.071428572 + y = 1.794265242 Solving 2.071428572 + y = 1.794265242 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + y = 1.794265242 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + y = 1.794265242 + -2.071428572 y = 1.794265242 + -2.071428572 Combine like terms: 1.794265242 + -2.071428572 = -0.27716333 y = -0.27716333 Simplifying y = -0.27716333Subproblem 2
y + 2.071428572 = -1.794265242 Simplifying y + 2.071428572 = -1.794265242 Reorder the terms: 2.071428572 + y = -1.794265242 Solving 2.071428572 + y = -1.794265242 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + y = -1.794265242 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + y = -1.794265242 + -2.071428572 y = -1.794265242 + -2.071428572 Combine like terms: -1.794265242 + -2.071428572 = -3.865693814 y = -3.865693814 Simplifying y = -3.865693814Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.27716333, -3.865693814}
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