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Simplifying 7y2 + -8y + -7 = 0 Reorder the terms: -7 + -8y + 7y2 = 0 Solving -7 + -8y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + -1.142857143y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.142857143y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -1.142857143y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.142857143y + y2 = 0 + 1 -1.142857143y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.142857143y + y2 = 1 The y term is -1.142857143y. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143y + 0.3265306123 + y2 = 1 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143y + y2 = 1 + 0.3265306123 Combine like terms: 1 + 0.3265306123 = 1.3265306123 0.3265306123 + -1.142857143y + y2 = 1.3265306123 Factor a perfect square on the left side: (y + -0.5714285715)(y + -0.5714285715) = 1.3265306123 Calculate the square root of the right side: 1.151751107 Break this problem into two subproblems by setting (y + -0.5714285715) equal to 1.151751107 and -1.151751107.Subproblem 1
y + -0.5714285715 = 1.151751107 Simplifying y + -0.5714285715 = 1.151751107 Reorder the terms: -0.5714285715 + y = 1.151751107 Solving -0.5714285715 + y = 1.151751107 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + y = 1.151751107 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + y = 1.151751107 + 0.5714285715 y = 1.151751107 + 0.5714285715 Combine like terms: 1.151751107 + 0.5714285715 = 1.7231796785 y = 1.7231796785 Simplifying y = 1.7231796785Subproblem 2
y + -0.5714285715 = -1.151751107 Simplifying y + -0.5714285715 = -1.151751107 Reorder the terms: -0.5714285715 + y = -1.151751107 Solving -0.5714285715 + y = -1.151751107 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + y = -1.151751107 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + y = -1.151751107 + 0.5714285715 y = -1.151751107 + 0.5714285715 Combine like terms: -1.151751107 + 0.5714285715 = -0.5803225355 y = -0.5803225355 Simplifying y = -0.5803225355Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.7231796785, -0.5803225355}
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