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Simplifying (y + -5)(y + 9) = 45 Reorder the terms: (-5 + y)(y + 9) = 45 Reorder the terms: (-5 + y)(9 + y) = 45 Multiply (-5 + y) * (9 + y) (-5(9 + y) + y(9 + y)) = 45 ((9 * -5 + y * -5) + y(9 + y)) = 45 ((-45 + -5y) + y(9 + y)) = 45 (-45 + -5y + (9 * y + y * y)) = 45 (-45 + -5y + (9y + y2)) = 45 Combine like terms: -5y + 9y = 4y (-45 + 4y + y2) = 45 Solving -45 + 4y + y2 = 45 Solving for variable 'y'. Reorder the terms: -45 + -45 + 4y + y2 = 45 + -45 Combine like terms: -45 + -45 = -90 -90 + 4y + y2 = 45 + -45 Combine like terms: 45 + -45 = 0 -90 + 4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 4y + 90 + y2 = 0 + 90 Reorder the terms: -90 + 90 + 4y + y2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 4y + y2 = 0 + 90 4y + y2 = 0 + 90 Combine like terms: 0 + 90 = 90 4y + y2 = 90 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 = 90 + 4 Reorder the terms: 4 + 4y + y2 = 90 + 4 Combine like terms: 90 + 4 = 94 4 + 4y + y2 = 94 Factor a perfect square on the left side: (y + 2)(y + 2) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (y + 2) equal to 9.695359715 and -9.695359715.Subproblem 1
y + 2 = 9.695359715 Simplifying y + 2 = 9.695359715 Reorder the terms: 2 + y = 9.695359715 Solving 2 + y = 9.695359715 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 = 9.695359715 + -2 Combine like terms: 2 + -2 = 0 0 + y = 9.695359715 + -2 y = 9.695359715 + -2 Combine like terms: 9.695359715 + -2 = 7.695359715 y = 7.695359715 Simplifying y = 7.695359715Subproblem 2
y + 2 = -9.695359715 Simplifying y + 2 = -9.695359715 Reorder the terms: 2 + y = -9.695359715 Solving 2 + y = -9.695359715 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 = -9.695359715 + -2 Combine like terms: 2 + -2 = 0 0 + y = -9.695359715 + -2 y = -9.695359715 + -2 Combine like terms: -9.695359715 + -2 = -11.695359715 y = -11.695359715 Simplifying y = -11.695359715Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.695359715, -11.695359715}
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