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Simplifying (-9y + -4y + -5) + (7y2 + y) = 0 Reorder the terms: (-5 + -9y + -4y) + (7y2 + y) = 0 Combine like terms: -9y + -4y = -13y (-5 + -13y) + (7y2 + y) = 0 Remove parenthesis around (-5 + -13y) -5 + -13y + (7y2 + y) = 0 Reorder the terms: -5 + -13y + (y + 7y2) = 0 Remove parenthesis around (y + 7y2) -5 + -13y + y + 7y2 = 0 Combine like terms: -13y + y = -12y -5 + -12y + 7y2 = 0 Solving -5 + -12y + 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'. -0.7142857143 + -1.714285714y + y2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -1.714285714y + 0.7142857143 + y2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -1.714285714y + y2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -1.714285714y + y2 = 0 + 0.7142857143 -1.714285714y + y2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -1.714285714y + y2 = 0.7142857143 The y term is -1.714285714y. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714y + 0.7346938773 + y2 = 0.7142857143 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714y + y2 = 0.7142857143 + 0.7346938773 Combine like terms: 0.7142857143 + 0.7346938773 = 1.4489795916 0.7346938773 + -1.714285714y + y2 = 1.4489795916 Factor a perfect square on the left side: (y + -0.857142857)(y + -0.857142857) = 1.4489795916 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (y + -0.857142857) equal to 1.203735682 and -1.203735682.Subproblem 1
y + -0.857142857 = 1.203735682 Simplifying y + -0.857142857 = 1.203735682 Reorder the terms: -0.857142857 + y = 1.203735682 Solving -0.857142857 + y = 1.203735682 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + y = 1.203735682 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + y = 1.203735682 + 0.857142857 y = 1.203735682 + 0.857142857 Combine like terms: 1.203735682 + 0.857142857 = 2.060878539 y = 2.060878539 Simplifying y = 2.060878539Subproblem 2
y + -0.857142857 = -1.203735682 Simplifying y + -0.857142857 = -1.203735682 Reorder the terms: -0.857142857 + y = -1.203735682 Solving -0.857142857 + y = -1.203735682 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + y = -1.203735682 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + y = -1.203735682 + 0.857142857 y = -1.203735682 + 0.857142857 Combine like terms: -1.203735682 + 0.857142857 = -0.346592825 y = -0.346592825 Simplifying y = -0.346592825Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.060878539, -0.346592825}
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