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Simplifying y2 + 4y + -176 = 0 Reorder the terms: -176 + 4y + y2 = 0 Solving -176 + 4y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '176' to each side of the equation. -176 + 4y + 176 + y2 = 0 + 176 Reorder the terms: -176 + 176 + 4y + y2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + 4y + y2 = 0 + 176 4y + y2 = 0 + 176 Combine like terms: 0 + 176 = 176 4y + y2 = 176 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 = 176 + 4 Reorder the terms: 4 + 4y + y2 = 176 + 4 Combine like terms: 176 + 4 = 180 4 + 4y + y2 = 180 Factor a perfect square on the left side: (y + 2)(y + 2) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (y + 2) equal to 13.416407865 and -13.416407865.Subproblem 1
y + 2 = 13.416407865 Simplifying y + 2 = 13.416407865 Reorder the terms: 2 + y = 13.416407865 Solving 2 + y = 13.416407865 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 = 13.416407865 + -2 Combine like terms: 2 + -2 = 0 0 + y = 13.416407865 + -2 y = 13.416407865 + -2 Combine like terms: 13.416407865 + -2 = 11.416407865 y = 11.416407865 Simplifying y = 11.416407865Subproblem 2
y + 2 = -13.416407865 Simplifying y + 2 = -13.416407865 Reorder the terms: 2 + y = -13.416407865 Solving 2 + y = -13.416407865 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 = -13.416407865 + -2 Combine like terms: 2 + -2 = 0 0 + y = -13.416407865 + -2 y = -13.416407865 + -2 Combine like terms: -13.416407865 + -2 = -15.416407865 y = -15.416407865 Simplifying y = -15.416407865Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.416407865, -15.416407865}
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