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Simplifying y2 + 17.88y + -20 = 0 Reorder the terms: -20 + 17.88y + y2 = 0 Solving -20 + 17.88y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 17.88y + 20 + y2 = 0 + 20 Reorder the terms: -20 + 20 + 17.88y + y2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 17.88y + y2 = 0 + 20 17.88y + y2 = 0 + 20 Combine like terms: 0 + 20 = 20 17.88y + y2 = 20 The y term is 17.88y. Take half its coefficient (8.94). Square it (79.9236) and add it to both sides. Add '79.9236' to each side of the equation. 17.88y + 79.9236 + y2 = 20 + 79.9236 Reorder the terms: 79.9236 + 17.88y + y2 = 20 + 79.9236 Combine like terms: 20 + 79.9236 = 99.9236 79.9236 + 17.88y + y2 = 99.9236 Factor a perfect square on the left side: (y + 8.94)(y + 8.94) = 99.9236 Calculate the square root of the right side: 9.99617927 Break this problem into two subproblems by setting (y + 8.94) equal to 9.99617927 and -9.99617927.Subproblem 1
y + 8.94 = 9.99617927 Simplifying y + 8.94 = 9.99617927 Reorder the terms: 8.94 + y = 9.99617927 Solving 8.94 + y = 9.99617927 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.94' to each side of the equation. 8.94 + -8.94 + y = 9.99617927 + -8.94 Combine like terms: 8.94 + -8.94 = 0.00 0.00 + y = 9.99617927 + -8.94 y = 9.99617927 + -8.94 Combine like terms: 9.99617927 + -8.94 = 1.05617927 y = 1.05617927 Simplifying y = 1.05617927Subproblem 2
y + 8.94 = -9.99617927 Simplifying y + 8.94 = -9.99617927 Reorder the terms: 8.94 + y = -9.99617927 Solving 8.94 + y = -9.99617927 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.94' to each side of the equation. 8.94 + -8.94 + y = -9.99617927 + -8.94 Combine like terms: 8.94 + -8.94 = 0.00 0.00 + y = -9.99617927 + -8.94 y = -9.99617927 + -8.94 Combine like terms: -9.99617927 + -8.94 = -18.93617927 y = -18.93617927 Simplifying y = -18.93617927Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.05617927, -18.93617927}
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