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Simplifying (5y + 2)(5y + 2) = 98 Reorder the terms: (2 + 5y)(5y + 2) = 98 Reorder the terms: (2 + 5y)(2 + 5y) = 98 Multiply (2 + 5y) * (2 + 5y) (2(2 + 5y) + 5y * (2 + 5y)) = 98 ((2 * 2 + 5y * 2) + 5y * (2 + 5y)) = 98 ((4 + 10y) + 5y * (2 + 5y)) = 98 (4 + 10y + (2 * 5y + 5y * 5y)) = 98 (4 + 10y + (10y + 25y2)) = 98 Combine like terms: 10y + 10y = 20y (4 + 20y + 25y2) = 98 Solving 4 + 20y + 25y2 = 98 Solving for variable 'y'. Reorder the terms: 4 + -98 + 20y + 25y2 = 98 + -98 Combine like terms: 4 + -98 = -94 -94 + 20y + 25y2 = 98 + -98 Combine like terms: 98 + -98 = 0 -94 + 20y + 25y2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -3.76 + 0.8y + y2 = 0 Move the constant term to the right: Add '3.76' to each side of the equation. -3.76 + 0.8y + 3.76 + y2 = 0 + 3.76 Reorder the terms: -3.76 + 3.76 + 0.8y + y2 = 0 + 3.76 Combine like terms: -3.76 + 3.76 = 0.00 0.00 + 0.8y + y2 = 0 + 3.76 0.8y + y2 = 0 + 3.76 Combine like terms: 0 + 3.76 = 3.76 0.8y + y2 = 3.76 The y term is 0.8y. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8y + 0.16 + y2 = 3.76 + 0.16 Reorder the terms: 0.16 + 0.8y + y2 = 3.76 + 0.16 Combine like terms: 3.76 + 0.16 = 3.92 0.16 + 0.8y + y2 = 3.92 Factor a perfect square on the left side: (y + 0.4)(y + 0.4) = 3.92 Calculate the square root of the right side: 1.979898987 Break this problem into two subproblems by setting (y + 0.4) equal to 1.979898987 and -1.979898987.Subproblem 1
y + 0.4 = 1.979898987 Simplifying y + 0.4 = 1.979898987 Reorder the terms: 0.4 + y = 1.979898987 Solving 0.4 + y = 1.979898987 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = 1.979898987 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = 1.979898987 + -0.4 y = 1.979898987 + -0.4 Combine like terms: 1.979898987 + -0.4 = 1.579898987 y = 1.579898987 Simplifying y = 1.579898987Subproblem 2
y + 0.4 = -1.979898987 Simplifying y + 0.4 = -1.979898987 Reorder the terms: 0.4 + y = -1.979898987 Solving 0.4 + y = -1.979898987 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = -1.979898987 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = -1.979898987 + -0.4 y = -1.979898987 + -0.4 Combine like terms: -1.979898987 + -0.4 = -2.379898987 y = -2.379898987 Simplifying y = -2.379898987Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.579898987, -2.379898987}
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