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Simplifying 25y2 + -16y + -32 = 0 Reorder the terms: -32 + -16y + 25y2 = 0 Solving -32 + -16y + 25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.28 + -0.64y + y2 = 0 Move the constant term to the right: Add '1.28' to each side of the equation. -1.28 + -0.64y + 1.28 + y2 = 0 + 1.28 Reorder the terms: -1.28 + 1.28 + -0.64y + y2 = 0 + 1.28 Combine like terms: -1.28 + 1.28 = 0.00 0.00 + -0.64y + y2 = 0 + 1.28 -0.64y + y2 = 0 + 1.28 Combine like terms: 0 + 1.28 = 1.28 -0.64y + y2 = 1.28 The y term is -0.64y. Take half its coefficient (-0.32). Square it (0.1024) and add it to both sides. Add '0.1024' to each side of the equation. -0.64y + 0.1024 + y2 = 1.28 + 0.1024 Reorder the terms: 0.1024 + -0.64y + y2 = 1.28 + 0.1024 Combine like terms: 1.28 + 0.1024 = 1.3824 0.1024 + -0.64y + y2 = 1.3824 Factor a perfect square on the left side: (y + -0.32)(y + -0.32) = 1.3824 Calculate the square root of the right side: 1.175755077 Break this problem into two subproblems by setting (y + -0.32) equal to 1.175755077 and -1.175755077.Subproblem 1
y + -0.32 = 1.175755077 Simplifying y + -0.32 = 1.175755077 Reorder the terms: -0.32 + y = 1.175755077 Solving -0.32 + y = 1.175755077 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.32' to each side of the equation. -0.32 + 0.32 + y = 1.175755077 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + y = 1.175755077 + 0.32 y = 1.175755077 + 0.32 Combine like terms: 1.175755077 + 0.32 = 1.495755077 y = 1.495755077 Simplifying y = 1.495755077Subproblem 2
y + -0.32 = -1.175755077 Simplifying y + -0.32 = -1.175755077 Reorder the terms: -0.32 + y = -1.175755077 Solving -0.32 + y = -1.175755077 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.32' to each side of the equation. -0.32 + 0.32 + y = -1.175755077 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + y = -1.175755077 + 0.32 y = -1.175755077 + 0.32 Combine like terms: -1.175755077 + 0.32 = -0.855755077 y = -0.855755077 Simplifying y = -0.855755077Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.495755077, -0.855755077}
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