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Simplifying y2 + 28y + -132 = 0 Reorder the terms: -132 + 28y + y2 = 0 Solving -132 + 28y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '132' to each side of the equation. -132 + 28y + 132 + y2 = 0 + 132 Reorder the terms: -132 + 132 + 28y + y2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + 28y + y2 = 0 + 132 28y + y2 = 0 + 132 Combine like terms: 0 + 132 = 132 28y + y2 = 132 The y term is 28y. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28y + 196 + y2 = 132 + 196 Reorder the terms: 196 + 28y + y2 = 132 + 196 Combine like terms: 132 + 196 = 328 196 + 28y + y2 = 328 Factor a perfect square on the left side: (y + 14)(y + 14) = 328 Calculate the square root of the right side: 18.110770276 Break this problem into two subproblems by setting (y + 14) equal to 18.110770276 and -18.110770276.Subproblem 1
y + 14 = 18.110770276 Simplifying y + 14 = 18.110770276 Reorder the terms: 14 + y = 18.110770276 Solving 14 + y = 18.110770276 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = 18.110770276 + -14 Combine like terms: 14 + -14 = 0 0 + y = 18.110770276 + -14 y = 18.110770276 + -14 Combine like terms: 18.110770276 + -14 = 4.110770276 y = 4.110770276 Simplifying y = 4.110770276Subproblem 2
y + 14 = -18.110770276 Simplifying y + 14 = -18.110770276 Reorder the terms: 14 + y = -18.110770276 Solving 14 + y = -18.110770276 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = -18.110770276 + -14 Combine like terms: 14 + -14 = 0 0 + y = -18.110770276 + -14 y = -18.110770276 + -14 Combine like terms: -18.110770276 + -14 = -32.110770276 y = -32.110770276 Simplifying y = -32.110770276Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.110770276, -32.110770276}
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