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Simplifying 36 + -60y + 25y2 + 16y2 + -60 + 50y + -4y + 19 = 0 Reorder the terms: 36 + -60 + 19 + -60y + 50y + -4y + 25y2 + 16y2 = 0 Combine like terms: 36 + -60 = -24 -24 + 19 + -60y + 50y + -4y + 25y2 + 16y2 = 0 Combine like terms: -24 + 19 = -5 -5 + -60y + 50y + -4y + 25y2 + 16y2 = 0 Combine like terms: -60y + 50y = -10y -5 + -10y + -4y + 25y2 + 16y2 = 0 Combine like terms: -10y + -4y = -14y -5 + -14y + 25y2 + 16y2 = 0 Combine like terms: 25y2 + 16y2 = 41y2 -5 + -14y + 41y2 = 0 Solving -5 + -14y + 41y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 41 the coefficient of the squared term: Divide each side by '41'. -0.1219512195 + -0.3414634146y + y2 = 0 Move the constant term to the right: Add '0.1219512195' to each side of the equation. -0.1219512195 + -0.3414634146y + 0.1219512195 + y2 = 0 + 0.1219512195 Reorder the terms: -0.1219512195 + 0.1219512195 + -0.3414634146y + y2 = 0 + 0.1219512195 Combine like terms: -0.1219512195 + 0.1219512195 = 0.0000000000 0.0000000000 + -0.3414634146y + y2 = 0 + 0.1219512195 -0.3414634146y + y2 = 0 + 0.1219512195 Combine like terms: 0 + 0.1219512195 = 0.1219512195 -0.3414634146y + y2 = 0.1219512195 The y term is -0.3414634146y. Take half its coefficient (-0.1707317073). Square it (0.02914931588) and add it to both sides. Add '0.02914931588' to each side of the equation. -0.3414634146y + 0.02914931588 + y2 = 0.1219512195 + 0.02914931588 Reorder the terms: 0.02914931588 + -0.3414634146y + y2 = 0.1219512195 + 0.02914931588 Combine like terms: 0.1219512195 + 0.02914931588 = 0.15110053538 0.02914931588 + -0.3414634146y + y2 = 0.15110053538 Factor a perfect square on the left side: (y + -0.1707317073)(y + -0.1707317073) = 0.15110053538 Calculate the square root of the right side: 0.388716523 Break this problem into two subproblems by setting (y + -0.1707317073) equal to 0.388716523 and -0.388716523.Subproblem 1
y + -0.1707317073 = 0.388716523 Simplifying y + -0.1707317073 = 0.388716523 Reorder the terms: -0.1707317073 + y = 0.388716523 Solving -0.1707317073 + y = 0.388716523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1707317073' to each side of the equation. -0.1707317073 + 0.1707317073 + y = 0.388716523 + 0.1707317073 Combine like terms: -0.1707317073 + 0.1707317073 = 0.0000000000 0.0000000000 + y = 0.388716523 + 0.1707317073 y = 0.388716523 + 0.1707317073 Combine like terms: 0.388716523 + 0.1707317073 = 0.5594482303 y = 0.5594482303 Simplifying y = 0.5594482303Subproblem 2
y + -0.1707317073 = -0.388716523 Simplifying y + -0.1707317073 = -0.388716523 Reorder the terms: -0.1707317073 + y = -0.388716523 Solving -0.1707317073 + y = -0.388716523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1707317073' to each side of the equation. -0.1707317073 + 0.1707317073 + y = -0.388716523 + 0.1707317073 Combine like terms: -0.1707317073 + 0.1707317073 = 0.0000000000 0.0000000000 + y = -0.388716523 + 0.1707317073 y = -0.388716523 + 0.1707317073 Combine like terms: -0.388716523 + 0.1707317073 = -0.2179848157 y = -0.2179848157 Simplifying y = -0.2179848157Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.5594482303, -0.2179848157}
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