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Simplifying (5y2 + 4y + -4) + -1(6y2 + -7y + -8) = 0 Reorder the terms: (-4 + 4y + 5y2) + -1(6y2 + -7y + -8) = 0 Remove parenthesis around (-4 + 4y + 5y2) -4 + 4y + 5y2 + -1(6y2 + -7y + -8) = 0 Reorder the terms: -4 + 4y + 5y2 + -1(-8 + -7y + 6y2) = 0 -4 + 4y + 5y2 + (-8 * -1 + -7y * -1 + 6y2 * -1) = 0 -4 + 4y + 5y2 + (8 + 7y + -6y2) = 0 Reorder the terms: -4 + 8 + 4y + 7y + 5y2 + -6y2 = 0 Combine like terms: -4 + 8 = 4 4 + 4y + 7y + 5y2 + -6y2 = 0 Combine like terms: 4y + 7y = 11y 4 + 11y + 5y2 + -6y2 = 0 Combine like terms: 5y2 + -6y2 = -1y2 4 + 11y + -1y2 = 0 Solving 4 + 11y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -11y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -11y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -11y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -11y + y2 = 0 + 4 -11y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -11y + y2 = 4 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = 4 + 30.25 Reorder the terms: 30.25 + -11y + y2 = 4 + 30.25 Combine like terms: 4 + 30.25 = 34.25 30.25 + -11y + y2 = 34.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (y + -5.5) equal to 5.852349955 and -5.852349955.Subproblem 1
y + -5.5 = 5.852349955 Simplifying y + -5.5 = 5.852349955 Reorder the terms: -5.5 + y = 5.852349955 Solving -5.5 + y = 5.852349955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 5.852349955 + 5.5 y = 5.852349955 + 5.5 Combine like terms: 5.852349955 + 5.5 = 11.352349955 y = 11.352349955 Simplifying y = 11.352349955Subproblem 2
y + -5.5 = -5.852349955 Simplifying y + -5.5 = -5.852349955 Reorder the terms: -5.5 + y = -5.852349955 Solving -5.5 + y = -5.852349955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -5.852349955 + 5.5 y = -5.852349955 + 5.5 Combine like terms: -5.852349955 + 5.5 = -0.352349955 y = -0.352349955 Simplifying y = -0.352349955Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.352349955, -0.352349955}
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