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Simplifying 1600y2 + -19.62y + -29.43 = 0 Reorder the terms: -29.43 + -19.62y + 1600y2 = 0 Solving -29.43 + -19.62y + 1600y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 1600 the coefficient of the squared term: Divide each side by '1600'. -0.01839375 + -0.0122625y + y2 = 0 Move the constant term to the right: Add '0.01839375' to each side of the equation. -0.01839375 + -0.0122625y + 0.01839375 + y2 = 0 + 0.01839375 Reorder the terms: -0.01839375 + 0.01839375 + -0.0122625y + y2 = 0 + 0.01839375 Combine like terms: -0.01839375 + 0.01839375 = 0.00000000 0.00000000 + -0.0122625y + y2 = 0 + 0.01839375 -0.0122625y + y2 = 0 + 0.01839375 Combine like terms: 0 + 0.01839375 = 0.01839375 -0.0122625y + y2 = 0.01839375 The y term is -0.0122625y. Take half its coefficient (-0.00613125). Square it (0.00003759222656) and add it to both sides. Add '0.00003759222656' to each side of the equation. -0.0122625y + 0.00003759222656 + y2 = 0.01839375 + 0.00003759222656 Reorder the terms: 0.00003759222656 + -0.0122625y + y2 = 0.01839375 + 0.00003759222656 Combine like terms: 0.01839375 + 0.00003759222656 = 0.01843134222656 0.00003759222656 + -0.0122625y + y2 = 0.01843134222656 Factor a perfect square on the left side: (y + -0.00613125)(y + -0.00613125) = 0.01843134222656 Calculate the square root of the right side: 0.135762079 Break this problem into two subproblems by setting (y + -0.00613125) equal to 0.135762079 and -0.135762079.Subproblem 1
y + -0.00613125 = 0.135762079 Simplifying y + -0.00613125 = 0.135762079 Reorder the terms: -0.00613125 + y = 0.135762079 Solving -0.00613125 + y = 0.135762079 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.00613125' to each side of the equation. -0.00613125 + 0.00613125 + y = 0.135762079 + 0.00613125 Combine like terms: -0.00613125 + 0.00613125 = 0.00000000 0.00000000 + y = 0.135762079 + 0.00613125 y = 0.135762079 + 0.00613125 Combine like terms: 0.135762079 + 0.00613125 = 0.141893329 y = 0.141893329 Simplifying y = 0.141893329Subproblem 2
y + -0.00613125 = -0.135762079 Simplifying y + -0.00613125 = -0.135762079 Reorder the terms: -0.00613125 + y = -0.135762079 Solving -0.00613125 + y = -0.135762079 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.00613125' to each side of the equation. -0.00613125 + 0.00613125 + y = -0.135762079 + 0.00613125 Combine like terms: -0.00613125 + 0.00613125 = 0.00000000 0.00000000 + y = -0.135762079 + 0.00613125 y = -0.135762079 + 0.00613125 Combine like terms: -0.135762079 + 0.00613125 = -0.129630829 y = -0.129630829 Simplifying y = -0.129630829Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.141893329, -0.129630829}
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