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Simplifying 8y2 + -7y + 7 + -14y2 + -7y + 2 = 0 Reorder the terms: 7 + 2 + -7y + -7y + 8y2 + -14y2 = 0 Combine like terms: 7 + 2 = 9 9 + -7y + -7y + 8y2 + -14y2 = 0 Combine like terms: -7y + -7y = -14y 9 + -14y + 8y2 + -14y2 = 0 Combine like terms: 8y2 + -14y2 = -6y2 9 + -14y + -6y2 = 0 Solving 9 + -14y + -6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.5 + 2.333333333y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 2.333333333y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 2.333333333y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 2.333333333y + y2 = 0 + 1.5 2.333333333y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 2.333333333y + y2 = 1.5 The y term is 2.333333333y. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333y + 1.361111112 + y2 = 1.5 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333y + y2 = 1.5 + 1.361111112 Combine like terms: 1.5 + 1.361111112 = 2.861111112 1.361111112 + 2.333333333y + y2 = 2.861111112 Factor a perfect square on the left side: (y + 1.166666667)(y + 1.166666667) = 2.861111112 Calculate the square root of the right side: 1.691481928 Break this problem into two subproblems by setting (y + 1.166666667) equal to 1.691481928 and -1.691481928.Subproblem 1
y + 1.166666667 = 1.691481928 Simplifying y + 1.166666667 = 1.691481928 Reorder the terms: 1.166666667 + y = 1.691481928 Solving 1.166666667 + y = 1.691481928 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + y = 1.691481928 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + y = 1.691481928 + -1.166666667 y = 1.691481928 + -1.166666667 Combine like terms: 1.691481928 + -1.166666667 = 0.524815261 y = 0.524815261 Simplifying y = 0.524815261Subproblem 2
y + 1.166666667 = -1.691481928 Simplifying y + 1.166666667 = -1.691481928 Reorder the terms: 1.166666667 + y = -1.691481928 Solving 1.166666667 + y = -1.691481928 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + y = -1.691481928 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + y = -1.691481928 + -1.166666667 y = -1.691481928 + -1.166666667 Combine like terms: -1.691481928 + -1.166666667 = -2.858148595 y = -2.858148595 Simplifying y = -2.858148595Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.524815261, -2.858148595}
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