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Simplifying y(y + 2) = 84 Reorder the terms: y(2 + y) = 84 (2 * y + y * y) = 84 (2y + y2) = 84 Solving 2y + y2 = 84 Solving for variable 'y'. Reorder the terms: -84 + 2y + y2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 2y + 84 + y2 = 0 + 84 Reorder the terms: -84 + 84 + 2y + y2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 2y + y2 = 0 + 84 2y + y2 = 0 + 84 Combine like terms: 0 + 84 = 84 2y + y2 = 84 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 84 + 1 Reorder the terms: 1 + 2y + y2 = 84 + 1 Combine like terms: 84 + 1 = 85 1 + 2y + y2 = 85 Factor a perfect square on the left side: (y + 1)(y + 1) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (y + 1) equal to 9.219544457 and -9.219544457.Subproblem 1
y + 1 = 9.219544457 Simplifying y + 1 = 9.219544457 Reorder the terms: 1 + y = 9.219544457 Solving 1 + y = 9.219544457 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 9.219544457 + -1 Combine like terms: 1 + -1 = 0 0 + y = 9.219544457 + -1 y = 9.219544457 + -1 Combine like terms: 9.219544457 + -1 = 8.219544457 y = 8.219544457 Simplifying y = 8.219544457Subproblem 2
y + 1 = -9.219544457 Simplifying y + 1 = -9.219544457 Reorder the terms: 1 + y = -9.219544457 Solving 1 + y = -9.219544457 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -9.219544457 + -1 Combine like terms: 1 + -1 = 0 0 + y = -9.219544457 + -1 y = -9.219544457 + -1 Combine like terms: -9.219544457 + -1 = -10.219544457 y = -10.219544457 Simplifying y = -10.219544457Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.219544457, -10.219544457}
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