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Simplifying y2 + 16y = -13 Reorder the terms: 16y + y2 = -13 Solving 16y + y2 = -13 Solving for variable 'y'. Reorder the terms: 13 + 16y + y2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + 16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 16y + -13 + y2 = 0 + -13 Reorder the terms: 13 + -13 + 16y + y2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 16y + y2 = 0 + -13 16y + y2 = 0 + -13 Combine like terms: 0 + -13 = -13 16y + y2 = -13 The y term is 16y. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16y + 64 + y2 = -13 + 64 Reorder the terms: 64 + 16y + y2 = -13 + 64 Combine like terms: -13 + 64 = 51 64 + 16y + y2 = 51 Factor a perfect square on the left side: (y + 8)(y + 8) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (y + 8) equal to 7.141428429 and -7.141428429.Subproblem 1
y + 8 = 7.141428429 Simplifying y + 8 = 7.141428429 Reorder the terms: 8 + y = 7.141428429 Solving 8 + y = 7.141428429 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 7.141428429 + -8 Combine like terms: 8 + -8 = 0 0 + y = 7.141428429 + -8 y = 7.141428429 + -8 Combine like terms: 7.141428429 + -8 = -0.858571571 y = -0.858571571 Simplifying y = -0.858571571Subproblem 2
y + 8 = -7.141428429 Simplifying y + 8 = -7.141428429 Reorder the terms: 8 + y = -7.141428429 Solving 8 + y = -7.141428429 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = -7.141428429 + -8 Combine like terms: 8 + -8 = 0 0 + y = -7.141428429 + -8 y = -7.141428429 + -8 Combine like terms: -7.141428429 + -8 = -15.141428429 y = -15.141428429 Simplifying y = -15.141428429Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.858571571, -15.141428429}
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