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Simplifying 25y2 + 49y + -4 = 0 Reorder the terms: -4 + 49y + 25y2 = 0 Solving -4 + 49y + 25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.16 + 1.96y + y2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + 1.96y + 0.16 + y2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + 1.96y + y2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + 1.96y + y2 = 0 + 0.16 1.96y + y2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 1.96y + y2 = 0.16 The y term is 1.96y. Take half its coefficient (0.98). Square it (0.9604) and add it to both sides. Add '0.9604' to each side of the equation. 1.96y + 0.9604 + y2 = 0.16 + 0.9604 Reorder the terms: 0.9604 + 1.96y + y2 = 0.16 + 0.9604 Combine like terms: 0.16 + 0.9604 = 1.1204 0.9604 + 1.96y + y2 = 1.1204 Factor a perfect square on the left side: (y + 0.98)(y + 0.98) = 1.1204 Calculate the square root of the right side: 1.05848949 Break this problem into two subproblems by setting (y + 0.98) equal to 1.05848949 and -1.05848949.Subproblem 1
y + 0.98 = 1.05848949 Simplifying y + 0.98 = 1.05848949 Reorder the terms: 0.98 + y = 1.05848949 Solving 0.98 + y = 1.05848949 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.98' to each side of the equation. 0.98 + -0.98 + y = 1.05848949 + -0.98 Combine like terms: 0.98 + -0.98 = 0.00 0.00 + y = 1.05848949 + -0.98 y = 1.05848949 + -0.98 Combine like terms: 1.05848949 + -0.98 = 0.07848949 y = 0.07848949 Simplifying y = 0.07848949Subproblem 2
y + 0.98 = -1.05848949 Simplifying y + 0.98 = -1.05848949 Reorder the terms: 0.98 + y = -1.05848949 Solving 0.98 + y = -1.05848949 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.98' to each side of the equation. 0.98 + -0.98 + y = -1.05848949 + -0.98 Combine like terms: 0.98 + -0.98 = 0.00 0.00 + y = -1.05848949 + -0.98 y = -1.05848949 + -0.98 Combine like terms: -1.05848949 + -0.98 = -2.03848949 y = -2.03848949 Simplifying y = -2.03848949Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.07848949, -2.03848949}
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