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Simplifying (y + 4) * y = 20 Reorder the terms: (4 + y) * y = 20 Reorder the terms for easier multiplication: y(4 + y) = 20 (4 * y + y * y) = 20 (4y + y2) = 20 Solving 4y + y2 = 20 Solving for variable 'y'. Reorder the terms: -20 + 4y + y2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 4y + 20 + y2 = 0 + 20 Reorder the terms: -20 + 20 + 4y + y2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 4y + y2 = 0 + 20 4y + y2 = 0 + 20 Combine like terms: 0 + 20 = 20 4y + y2 = 20 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 = 20 + 4 Reorder the terms: 4 + 4y + y2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + 4y + y2 = 24 Factor a perfect square on the left side: (y + 2)(y + 2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (y + 2) equal to 4.898979486 and -4.898979486.Subproblem 1
y + 2 = 4.898979486 Simplifying y + 2 = 4.898979486 Reorder the terms: 2 + y = 4.898979486 Solving 2 + y = 4.898979486 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 = 4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + y = 4.898979486 + -2 y = 4.898979486 + -2 Combine like terms: 4.898979486 + -2 = 2.898979486 y = 2.898979486 Simplifying y = 2.898979486Subproblem 2
y + 2 = -4.898979486 Simplifying y + 2 = -4.898979486 Reorder the terms: 2 + y = -4.898979486 Solving 2 + y = -4.898979486 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 = -4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + y = -4.898979486 + -2 y = -4.898979486 + -2 Combine like terms: -4.898979486 + -2 = -6.898979486 y = -6.898979486 Simplifying y = -6.898979486Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.898979486, -6.898979486}
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