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Simplifying y2 + -16.9y + -29.6 = 0 Reorder the terms: -29.6 + -16.9y + y2 = 0 Solving -29.6 + -16.9y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '29.6' to each side of the equation. -29.6 + -16.9y + 29.6 + y2 = 0 + 29.6 Reorder the terms: -29.6 + 29.6 + -16.9y + y2 = 0 + 29.6 Combine like terms: -29.6 + 29.6 = 0.0 0.0 + -16.9y + y2 = 0 + 29.6 -16.9y + y2 = 0 + 29.6 Combine like terms: 0 + 29.6 = 29.6 -16.9y + y2 = 29.6 The y term is -16.9y. Take half its coefficient (-8.45). Square it (71.4025) and add it to both sides. Add '71.4025' to each side of the equation. -16.9y + 71.4025 + y2 = 29.6 + 71.4025 Reorder the terms: 71.4025 + -16.9y + y2 = 29.6 + 71.4025 Combine like terms: 29.6 + 71.4025 = 101.0025 71.4025 + -16.9y + y2 = 101.0025 Factor a perfect square on the left side: (y + -8.45)(y + -8.45) = 101.0025 Calculate the square root of the right side: 10.05 Break this problem into two subproblems by setting (y + -8.45) equal to 10.05 and -10.05.Subproblem 1
y + -8.45 = 10.05 Simplifying y + -8.45 = 10.05 Reorder the terms: -8.45 + y = 10.05 Solving -8.45 + y = 10.05 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.45' to each side of the equation. -8.45 + 8.45 + y = 10.05 + 8.45 Combine like terms: -8.45 + 8.45 = 0.00 0.00 + y = 10.05 + 8.45 y = 10.05 + 8.45 Combine like terms: 10.05 + 8.45 = 18.5 y = 18.5 Simplifying y = 18.5Subproblem 2
y + -8.45 = -10.05 Simplifying y + -8.45 = -10.05 Reorder the terms: -8.45 + y = -10.05 Solving -8.45 + y = -10.05 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.45' to each side of the equation. -8.45 + 8.45 + y = -10.05 + 8.45 Combine like terms: -8.45 + 8.45 = 0.00 0.00 + y = -10.05 + 8.45 y = -10.05 + 8.45 Combine like terms: -10.05 + 8.45 = -1.6 y = -1.6 Simplifying y = -1.6Solution
The solution to the problem is based on the solutions from the subproblems. y = {18.5, -1.6}
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