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Simplifying 4(y2 + 4y + 4) = 125 Reorder the terms: 4(4 + 4y + y2) = 125 (4 * 4 + 4y * 4 + y2 * 4) = 125 (16 + 16y + 4y2) = 125 Solving 16 + 16y + 4y2 = 125 Solving for variable 'y'. Reorder the terms: 16 + -125 + 16y + 4y2 = 125 + -125 Combine like terms: 16 + -125 = -109 -109 + 16y + 4y2 = 125 + -125 Combine like terms: 125 + -125 = 0 -109 + 16y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -27.25 + 4y + y2 = 0 Move the constant term to the right: Add '27.25' to each side of the equation. -27.25 + 4y + 27.25 + y2 = 0 + 27.25 Reorder the terms: -27.25 + 27.25 + 4y + y2 = 0 + 27.25 Combine like terms: -27.25 + 27.25 = 0.00 0.00 + 4y + y2 = 0 + 27.25 4y + y2 = 0 + 27.25 Combine like terms: 0 + 27.25 = 27.25 4y + y2 = 27.25 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 27.25 + 4 Reorder the terms: 4 + 4y + y2 = 27.25 + 4 Combine like terms: 27.25 + 4 = 31.25 4 + 4y + y2 = 31.25 Factor a perfect square on the left side: (y + 2)(y + 2) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (y + 2) equal to 5.590169944 and -5.590169944.Subproblem 1
y + 2 = 5.590169944 Simplifying y + 2 = 5.590169944 Reorder the terms: 2 + y = 5.590169944 Solving 2 + y = 5.590169944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 5.590169944 + -2 Combine like terms: 2 + -2 = 0 0 + y = 5.590169944 + -2 y = 5.590169944 + -2 Combine like terms: 5.590169944 + -2 = 3.590169944 y = 3.590169944 Simplifying y = 3.590169944Subproblem 2
y + 2 = -5.590169944 Simplifying y + 2 = -5.590169944 Reorder the terms: 2 + y = -5.590169944 Solving 2 + y = -5.590169944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -5.590169944 + -2 Combine like terms: 2 + -2 = 0 0 + y = -5.590169944 + -2 y = -5.590169944 + -2 Combine like terms: -5.590169944 + -2 = -7.590169944 y = -7.590169944 Simplifying y = -7.590169944Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.590169944, -7.590169944}
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