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Simplifying y2 + 70y + 75 = 0 Reorder the terms: 75 + 70y + y2 = 0 Solving 75 + 70y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + 70y + -75 + y2 = 0 + -75 Reorder the terms: 75 + -75 + 70y + y2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + 70y + y2 = 0 + -75 70y + y2 = 0 + -75 Combine like terms: 0 + -75 = -75 70y + y2 = -75 The y term is 70y. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70y + 1225 + y2 = -75 + 1225 Reorder the terms: 1225 + 70y + y2 = -75 + 1225 Combine like terms: -75 + 1225 = 1150 1225 + 70y + y2 = 1150 Factor a perfect square on the left side: (y + 35)(y + 35) = 1150 Calculate the square root of the right side: 33.911649916 Break this problem into two subproblems by setting (y + 35) equal to 33.911649916 and -33.911649916.Subproblem 1
y + 35 = 33.911649916 Simplifying y + 35 = 33.911649916 Reorder the terms: 35 + y = 33.911649916 Solving 35 + y = 33.911649916 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + y = 33.911649916 + -35 Combine like terms: 35 + -35 = 0 0 + y = 33.911649916 + -35 y = 33.911649916 + -35 Combine like terms: 33.911649916 + -35 = -1.088350084 y = -1.088350084 Simplifying y = -1.088350084Subproblem 2
y + 35 = -33.911649916 Simplifying y + 35 = -33.911649916 Reorder the terms: 35 + y = -33.911649916 Solving 35 + y = -33.911649916 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + y = -33.911649916 + -35 Combine like terms: 35 + -35 = 0 0 + y = -33.911649916 + -35 y = -33.911649916 + -35 Combine like terms: -33.911649916 + -35 = -68.911649916 y = -68.911649916 Simplifying y = -68.911649916Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.088350084, -68.911649916}
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