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Simplifying (4y2 + -9) + -1(-5y2 + 6y + -2) = 0 Reorder the terms: (-9 + 4y2) + -1(-5y2 + 6y + -2) = 0 Remove parenthesis around (-9 + 4y2) -9 + 4y2 + -1(-5y2 + 6y + -2) = 0 Reorder the terms: -9 + 4y2 + -1(-2 + 6y + -5y2) = 0 -9 + 4y2 + (-2 * -1 + 6y * -1 + -5y2 * -1) = 0 -9 + 4y2 + (2 + -6y + 5y2) = 0 Reorder the terms: -9 + 2 + -6y + 4y2 + 5y2 = 0 Combine like terms: -9 + 2 = -7 -7 + -6y + 4y2 + 5y2 = 0 Combine like terms: 4y2 + 5y2 = 9y2 -7 + -6y + 9y2 = 0 Solving -7 + -6y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + -0.6666666667y + y2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -0.6666666667y + 0.7777777778 + y2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -0.6666666667y + y2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -0.6666666667y + y2 = 0 + 0.7777777778 -0.6666666667y + y2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -0.6666666667y + y2 = 0.7777777778 The y term is -0.6666666667y. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667y + 0.1111111112 + y2 = 0.7777777778 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667y + y2 = 0.7777777778 + 0.1111111112 Combine like terms: 0.7777777778 + 0.1111111112 = 0.888888889 0.1111111112 + -0.6666666667y + y2 = 0.888888889 Factor a perfect square on the left side: (y + -0.3333333334)(y + -0.3333333334) = 0.888888889 Calculate the square root of the right side: 0.942809042 Break this problem into two subproblems by setting (y + -0.3333333334) equal to 0.942809042 and -0.942809042.Subproblem 1
y + -0.3333333334 = 0.942809042 Simplifying y + -0.3333333334 = 0.942809042 Reorder the terms: -0.3333333334 + y = 0.942809042 Solving -0.3333333334 + y = 0.942809042 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + y = 0.942809042 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + y = 0.942809042 + 0.3333333334 y = 0.942809042 + 0.3333333334 Combine like terms: 0.942809042 + 0.3333333334 = 1.2761423754 y = 1.2761423754 Simplifying y = 1.2761423754Subproblem 2
y + -0.3333333334 = -0.942809042 Simplifying y + -0.3333333334 = -0.942809042 Reorder the terms: -0.3333333334 + y = -0.942809042 Solving -0.3333333334 + y = -0.942809042 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + y = -0.942809042 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + y = -0.942809042 + 0.3333333334 y = -0.942809042 + 0.3333333334 Combine like terms: -0.942809042 + 0.3333333334 = -0.6094757086 y = -0.6094757086 Simplifying y = -0.6094757086Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.2761423754, -0.6094757086}
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