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Simplifying 2y2 + 20y + 49 = 0 Reorder the terms: 49 + 20y + 2y2 = 0 Solving 49 + 20y + 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'. 24.5 + 10y + y2 = 0 Move the constant term to the right: Add '-24.5' to each side of the equation. 24.5 + 10y + -24.5 + y2 = 0 + -24.5 Reorder the terms: 24.5 + -24.5 + 10y + y2 = 0 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + 10y + y2 = 0 + -24.5 10y + y2 = 0 + -24.5 Combine like terms: 0 + -24.5 = -24.5 10y + y2 = -24.5 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = -24.5 + 25 Reorder the terms: 25 + 10y + y2 = -24.5 + 25 Combine like terms: -24.5 + 25 = 0.5 25 + 10y + y2 = 0.5 Factor a perfect square on the left side: (y + 5)(y + 5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (y + 5) equal to 0.707106781 and -0.707106781.Subproblem 1
y + 5 = 0.707106781 Simplifying y + 5 = 0.707106781 Reorder the terms: 5 + y = 0.707106781 Solving 5 + y = 0.707106781 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0.707106781 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0.707106781 + -5 y = 0.707106781 + -5 Combine like terms: 0.707106781 + -5 = -4.292893219 y = -4.292893219 Simplifying y = -4.292893219Subproblem 2
y + 5 = -0.707106781 Simplifying y + 5 = -0.707106781 Reorder the terms: 5 + y = -0.707106781 Solving 5 + y = -0.707106781 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -0.707106781 + -5 Combine like terms: 5 + -5 = 0 0 + y = -0.707106781 + -5 y = -0.707106781 + -5 Combine like terms: -0.707106781 + -5 = -5.707106781 y = -5.707106781 Simplifying y = -5.707106781Solution
The solution to the problem is based on the solutions from the subproblems. y = {-4.292893219, -5.707106781}
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