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Simplifying 32(y + 10) * 29y + 3(y + -5) = 0 Reorder the terms: 32(10 + y) * 29y + 3(y + -5) = 0 Reorder the terms for easier multiplication: 32 * 29y(10 + y) + 3(y + -5) = 0 Multiply 32 * 29 928y(10 + y) + 3(y + -5) = 0 (10 * 928y + y * 928y) + 3(y + -5) = 0 (9280y + 928y2) + 3(y + -5) = 0 Reorder the terms: 9280y + 928y2 + 3(-5 + y) = 0 9280y + 928y2 + (-5 * 3 + y * 3) = 0 9280y + 928y2 + (-15 + 3y) = 0 Reorder the terms: -15 + 9280y + 3y + 928y2 = 0 Combine like terms: 9280y + 3y = 9283y -15 + 9283y + 928y2 = 0 Solving -15 + 9283y + 928y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 928 the coefficient of the squared term: Divide each side by '928'. -0.0161637931 + 10.00323276y + y2 = 0 Move the constant term to the right: Add '0.0161637931' to each side of the equation. -0.0161637931 + 10.00323276y + 0.0161637931 + y2 = 0 + 0.0161637931 Reorder the terms: -0.0161637931 + 0.0161637931 + 10.00323276y + y2 = 0 + 0.0161637931 Combine like terms: -0.0161637931 + 0.0161637931 = 0.0000000000 0.0000000000 + 10.00323276y + y2 = 0 + 0.0161637931 10.00323276y + y2 = 0 + 0.0161637931 Combine like terms: 0 + 0.0161637931 = 0.0161637931 10.00323276y + y2 = 0.0161637931 The y term is 10.00323276y. Take half its coefficient (5.00161638). Square it (25.01616641) and add it to both sides. Add '25.01616641' to each side of the equation. 10.00323276y + 25.01616641 + y2 = 0.0161637931 + 25.01616641 Reorder the terms: 25.01616641 + 10.00323276y + y2 = 0.0161637931 + 25.01616641 Combine like terms: 0.0161637931 + 25.01616641 = 25.0323302031 25.01616641 + 10.00323276y + y2 = 25.0323302031 Factor a perfect square on the left side: (y + 5.00161638)(y + 5.00161638) = 25.0323302031 Calculate the square root of the right side: 5.003231976 Break this problem into two subproblems by setting (y + 5.00161638) equal to 5.003231976 and -5.003231976.Subproblem 1
y + 5.00161638 = 5.003231976 Simplifying y + 5.00161638 = 5.003231976 Reorder the terms: 5.00161638 + y = 5.003231976 Solving 5.00161638 + y = 5.003231976 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.00161638' to each side of the equation. 5.00161638 + -5.00161638 + y = 5.003231976 + -5.00161638 Combine like terms: 5.00161638 + -5.00161638 = 0.00000000 0.00000000 + y = 5.003231976 + -5.00161638 y = 5.003231976 + -5.00161638 Combine like terms: 5.003231976 + -5.00161638 = 0.001615596 y = 0.001615596 Simplifying y = 0.001615596Subproblem 2
y + 5.00161638 = -5.003231976 Simplifying y + 5.00161638 = -5.003231976 Reorder the terms: 5.00161638 + y = -5.003231976 Solving 5.00161638 + y = -5.003231976 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.00161638' to each side of the equation. 5.00161638 + -5.00161638 + y = -5.003231976 + -5.00161638 Combine like terms: 5.00161638 + -5.00161638 = 0.00000000 0.00000000 + y = -5.003231976 + -5.00161638 y = -5.003231976 + -5.00161638 Combine like terms: -5.003231976 + -5.00161638 = -10.004848356 y = -10.004848356 Simplifying y = -10.004848356Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.001615596, -10.004848356}
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