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Simplifying 2y2 + 21y + -10 = 0 Reorder the terms: -10 + 21y + 2y2 = 0 Solving -10 + 21y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 10.5y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 10.5y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + 10.5y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 10.5y + y2 = 0 + 5 10.5y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 10.5y + y2 = 5 The y term is 10.5y. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5y + 27.5625 + y2 = 5 + 27.5625 Reorder the terms: 27.5625 + 10.5y + y2 = 5 + 27.5625 Combine like terms: 5 + 27.5625 = 32.5625 27.5625 + 10.5y + y2 = 32.5625 Factor a perfect square on the left side: (y + 5.25)(y + 5.25) = 32.5625 Calculate the square root of the right side: 5.706356105 Break this problem into two subproblems by setting (y + 5.25) equal to 5.706356105 and -5.706356105.Subproblem 1
y + 5.25 = 5.706356105 Simplifying y + 5.25 = 5.706356105 Reorder the terms: 5.25 + y = 5.706356105 Solving 5.25 + y = 5.706356105 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + y = 5.706356105 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + y = 5.706356105 + -5.25 y = 5.706356105 + -5.25 Combine like terms: 5.706356105 + -5.25 = 0.456356105 y = 0.456356105 Simplifying y = 0.456356105Subproblem 2
y + 5.25 = -5.706356105 Simplifying y + 5.25 = -5.706356105 Reorder the terms: 5.25 + y = -5.706356105 Solving 5.25 + y = -5.706356105 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + y = -5.706356105 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + y = -5.706356105 + -5.25 y = -5.706356105 + -5.25 Combine like terms: -5.706356105 + -5.25 = -10.956356105 y = -10.956356105 Simplifying y = -10.956356105Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.456356105, -10.956356105}
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