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Simplifying 7Y2 + 7Y + -18 = 0 Reorder the terms: -18 + 7Y + 7Y2 = 0 Solving -18 + 7Y + 7Y2 = 0 Solving for variable 'Y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + Y + Y2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + Y + 2.571428571 + Y2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + Y + Y2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + Y + Y2 = 0 + 2.571428571 Y + Y2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 Y + Y2 = 2.571428571 The Y term is Y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + Y2 = 2.571428571 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + Y2 = 2.571428571 + 0.25 Combine like terms: 2.571428571 + 0.25 = 2.821428571 1.25 + Y2 = 2.821428571 Factor a perfect square on the left side: (Y + 0.5)(Y + 0.5) = 2.821428571 Calculate the square root of the right side: 1.679710859 Break this problem into two subproblems by setting (Y + 0.5) equal to 1.679710859 and -1.679710859.Subproblem 1
Y + 0.5 = 1.679710859 Simplifying Y + 0.5 = 1.679710859 Reorder the terms: 0.5 + Y = 1.679710859 Solving 0.5 + Y = 1.679710859 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + Y = 1.679710859 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + Y = 1.679710859 + -0.5 Y = 1.679710859 + -0.5 Combine like terms: 1.679710859 + -0.5 = 1.179710859 Y = 1.179710859 Simplifying Y = 1.179710859Subproblem 2
Y + 0.5 = -1.679710859 Simplifying Y + 0.5 = -1.679710859 Reorder the terms: 0.5 + Y = -1.679710859 Solving 0.5 + Y = -1.679710859 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + Y = -1.679710859 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + Y = -1.679710859 + -0.5 Y = -1.679710859 + -0.5 Combine like terms: -1.679710859 + -0.5 = -2.179710859 Y = -2.179710859 Simplifying Y = -2.179710859Solution
The solution to the problem is based on the solutions from the subproblems. Y = {1.179710859, -2.179710859}
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