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Simplifying (2y2 + 5y + -2) + -1(-3y + 7) = 0 Reorder the terms: (-2 + 5y + 2y2) + -1(-3y + 7) = 0 Remove parenthesis around (-2 + 5y + 2y2) -2 + 5y + 2y2 + -1(-3y + 7) = 0 Reorder the terms: -2 + 5y + 2y2 + -1(7 + -3y) = 0 -2 + 5y + 2y2 + (7 * -1 + -3y * -1) = 0 -2 + 5y + 2y2 + (-7 + 3y) = 0 Reorder the terms: -2 + -7 + 5y + 3y + 2y2 = 0 Combine like terms: -2 + -7 = -9 -9 + 5y + 3y + 2y2 = 0 Combine like terms: 5y + 3y = 8y -9 + 8y + 2y2 = 0 Solving -9 + 8y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 4y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 4y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 4y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 4y + y2 = 0 + 4.5 4y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 4y + y2 = 4.5 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 4.5 + 4 Reorder the terms: 4 + 4y + y2 = 4.5 + 4 Combine like terms: 4.5 + 4 = 8.5 4 + 4y + y2 = 8.5 Factor a perfect square on the left side: (y + 2)(y + 2) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (y + 2) equal to 2.915475947 and -2.915475947.Subproblem 1
y + 2 = 2.915475947 Simplifying y + 2 = 2.915475947 Reorder the terms: 2 + y = 2.915475947 Solving 2 + y = 2.915475947 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + y = 2.915475947 + -2 y = 2.915475947 + -2 Combine like terms: 2.915475947 + -2 = 0.915475947 y = 0.915475947 Simplifying y = 0.915475947Subproblem 2
y + 2 = -2.915475947 Simplifying y + 2 = -2.915475947 Reorder the terms: 2 + y = -2.915475947 Solving 2 + y = -2.915475947 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + y = -2.915475947 + -2 y = -2.915475947 + -2 Combine like terms: -2.915475947 + -2 = -4.915475947 y = -4.915475947 Simplifying y = -4.915475947Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.915475947, -4.915475947}
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