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Simplifying 400y + 4y2 = 9216 Solving 400y + 4y2 = 9216 Solving for variable 'y'. Reorder the terms: -9216 + 400y + 4y2 = 9216 + -9216 Combine like terms: 9216 + -9216 = 0 -9216 + 400y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2304 + 100y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2304 + 100y + y2)' equal to zero and attempt to solve: Simplifying -2304 + 100y + y2 = 0 Solving -2304 + 100y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '2304' to each side of the equation. -2304 + 100y + 2304 + y2 = 0 + 2304 Reorder the terms: -2304 + 2304 + 100y + y2 = 0 + 2304 Combine like terms: -2304 + 2304 = 0 0 + 100y + y2 = 0 + 2304 100y + y2 = 0 + 2304 Combine like terms: 0 + 2304 = 2304 100y + y2 = 2304 The y term is 100y. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100y + 2500 + y2 = 2304 + 2500 Reorder the terms: 2500 + 100y + y2 = 2304 + 2500 Combine like terms: 2304 + 2500 = 4804 2500 + 100y + y2 = 4804 Factor a perfect square on the left side: (y + 50)(y + 50) = 4804 Calculate the square root of the right side: 69.310893805 Break this problem into two subproblems by setting (y + 50) equal to 69.310893805 and -69.310893805.Subproblem 1
y + 50 = 69.310893805 Simplifying y + 50 = 69.310893805 Reorder the terms: 50 + y = 69.310893805 Solving 50 + y = 69.310893805 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + y = 69.310893805 + -50 Combine like terms: 50 + -50 = 0 0 + y = 69.310893805 + -50 y = 69.310893805 + -50 Combine like terms: 69.310893805 + -50 = 19.310893805 y = 19.310893805 Simplifying y = 19.310893805Subproblem 2
y + 50 = -69.310893805 Simplifying y + 50 = -69.310893805 Reorder the terms: 50 + y = -69.310893805 Solving 50 + y = -69.310893805 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + y = -69.310893805 + -50 Combine like terms: 50 + -50 = 0 0 + y = -69.310893805 + -50 y = -69.310893805 + -50 Combine like terms: -69.310893805 + -50 = -119.310893805 y = -119.310893805 Simplifying y = -119.310893805Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.310893805, -119.310893805}Solution
y = {19.310893805, -119.310893805}
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