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Simplifying (7y2 + 5y + -7) + -1(-3y + 3) = 0 Reorder the terms: (-7 + 5y + 7y2) + -1(-3y + 3) = 0 Remove parenthesis around (-7 + 5y + 7y2) -7 + 5y + 7y2 + -1(-3y + 3) = 0 Reorder the terms: -7 + 5y + 7y2 + -1(3 + -3y) = 0 -7 + 5y + 7y2 + (3 * -1 + -3y * -1) = 0 -7 + 5y + 7y2 + (-3 + 3y) = 0 Reorder the terms: -7 + -3 + 5y + 3y + 7y2 = 0 Combine like terms: -7 + -3 = -10 -10 + 5y + 3y + 7y2 = 0 Combine like terms: 5y + 3y = 8y -10 + 8y + 7y2 = 0 Solving -10 + 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'. -1.428571429 + 1.142857143y + y2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 1.142857143y + 1.428571429 + y2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 1.142857143y + y2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 1.142857143y + y2 = 0 + 1.428571429 1.142857143y + y2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 1.142857143y + y2 = 1.428571429 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 = 1.428571429 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143y + y2 = 1.428571429 + 0.3265306123 Combine like terms: 1.428571429 + 0.3265306123 = 1.7551020413 0.3265306123 + 1.142857143y + y2 = 1.7551020413 Factor a perfect square on the left side: (y + 0.5714285715)(y + 0.5714285715) = 1.7551020413 Calculate the square root of the right side: 1.324802642 Break this problem into two subproblems by setting (y + 0.5714285715) equal to 1.324802642 and -1.324802642.Subproblem 1
y + 0.5714285715 = 1.324802642 Simplifying y + 0.5714285715 = 1.324802642 Reorder the terms: 0.5714285715 + y = 1.324802642 Solving 0.5714285715 + y = 1.324802642 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 = 1.324802642 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + y = 1.324802642 + -0.5714285715 y = 1.324802642 + -0.5714285715 Combine like terms: 1.324802642 + -0.5714285715 = 0.7533740705 y = 0.7533740705 Simplifying y = 0.7533740705Subproblem 2
y + 0.5714285715 = -1.324802642 Simplifying y + 0.5714285715 = -1.324802642 Reorder the terms: 0.5714285715 + y = -1.324802642 Solving 0.5714285715 + y = -1.324802642 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 = -1.324802642 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + y = -1.324802642 + -0.5714285715 y = -1.324802642 + -0.5714285715 Combine like terms: -1.324802642 + -0.5714285715 = -1.8962312135 y = -1.8962312135 Simplifying y = -1.8962312135Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.7533740705, -1.8962312135}
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