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Simplifying 4y(y + 2) = 7 Reorder the terms: 4y(2 + y) = 7 (2 * 4y + y * 4y) = 7 (8y + 4y2) = 7 Solving 8y + 4y2 = 7 Solving for variable 'y'. Reorder the terms: -7 + 8y + 4y2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 8y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 2y + y2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 2y + 1.75 + y2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 2y + y2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 2y + y2 = 0 + 1.75 2y + y2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 2y + y2 = 1.75 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 1.75 + 1 Reorder the terms: 1 + 2y + y2 = 1.75 + 1 Combine like terms: 1.75 + 1 = 2.75 1 + 2y + y2 = 2.75 Factor a perfect square on the left side: (y + 1)(y + 1) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (y + 1) equal to 1.658312395 and -1.658312395.Subproblem 1
y + 1 = 1.658312395 Simplifying y + 1 = 1.658312395 Reorder the terms: 1 + y = 1.658312395 Solving 1 + y = 1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 1.658312395 + -1 Combine like terms: 1 + -1 = 0 0 + y = 1.658312395 + -1 y = 1.658312395 + -1 Combine like terms: 1.658312395 + -1 = 0.658312395 y = 0.658312395 Simplifying y = 0.658312395Subproblem 2
y + 1 = -1.658312395 Simplifying y + 1 = -1.658312395 Reorder the terms: 1 + y = -1.658312395 Solving 1 + y = -1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -1.658312395 + -1 Combine like terms: 1 + -1 = 0 0 + y = -1.658312395 + -1 y = -1.658312395 + -1 Combine like terms: -1.658312395 + -1 = -2.658312395 y = -2.658312395 Simplifying y = -2.658312395Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.658312395, -2.658312395}
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