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Simplifying (y + -5)(y + -9) = 15 Reorder the terms: (-5 + y)(y + -9) = 15 Reorder the terms: (-5 + y)(-9 + y) = 15 Multiply (-5 + y) * (-9 + y) (-5(-9 + y) + y(-9 + y)) = 15 ((-9 * -5 + y * -5) + y(-9 + y)) = 15 ((45 + -5y) + y(-9 + y)) = 15 (45 + -5y + (-9 * y + y * y)) = 15 (45 + -5y + (-9y + y2)) = 15 Combine like terms: -5y + -9y = -14y (45 + -14y + y2) = 15 Solving 45 + -14y + y2 = 15 Solving for variable 'y'. Reorder the terms: 45 + -15 + -14y + y2 = 15 + -15 Combine like terms: 45 + -15 = 30 30 + -14y + y2 = 15 + -15 Combine like terms: 15 + -15 = 0 30 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -14y + -30 + y2 = 0 + -30 Reorder the terms: 30 + -30 + -14y + y2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -14y + y2 = 0 + -30 -14y + y2 = 0 + -30 Combine like terms: 0 + -30 = -30 -14y + y2 = -30 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = -30 + 49 Reorder the terms: 49 + -14y + y2 = -30 + 49 Combine like terms: -30 + 49 = 19 49 + -14y + y2 = 19 Factor a perfect square on the left side: (y + -7)(y + -7) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (y + -7) equal to 4.358898944 and -4.358898944.Subproblem 1
y + -7 = 4.358898944 Simplifying y + -7 = 4.358898944 Reorder the terms: -7 + y = 4.358898944 Solving -7 + y = 4.358898944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 4.358898944 + 7 Combine like terms: -7 + 7 = 0 0 + y = 4.358898944 + 7 y = 4.358898944 + 7 Combine like terms: 4.358898944 + 7 = 11.358898944 y = 11.358898944 Simplifying y = 11.358898944Subproblem 2
y + -7 = -4.358898944 Simplifying y + -7 = -4.358898944 Reorder the terms: -7 + y = -4.358898944 Solving -7 + y = -4.358898944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -4.358898944 + 7 Combine like terms: -7 + 7 = 0 0 + y = -4.358898944 + 7 y = -4.358898944 + 7 Combine like terms: -4.358898944 + 7 = 2.641101056 y = 2.641101056 Simplifying y = 2.641101056Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.358898944, 2.641101056}
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