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Simplifying 4y2 + 8y + 3 = 12 Reorder the terms: 3 + 8y + 4y2 = 12 Solving 3 + 8y + 4y2 = 12 Solving for variable 'y'. Reorder the terms: 3 + -12 + 8y + 4y2 = 12 + -12 Combine like terms: 3 + -12 = -9 -9 + 8y + 4y2 = 12 + -12 Combine like terms: 12 + -12 = 0 -9 + 8y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 2y + y2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 2y + 2.25 + y2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 2y + y2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 2y + y2 = 0 + 2.25 2y + y2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 2y + y2 = 2.25 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 = 2.25 + 1 Reorder the terms: 1 + 2y + y2 = 2.25 + 1 Combine like terms: 2.25 + 1 = 3.25 1 + 2y + y2 = 3.25 Factor a perfect square on the left side: (y + 1)(y + 1) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (y + 1) equal to 1.802775638 and -1.802775638.Subproblem 1
y + 1 = 1.802775638 Simplifying y + 1 = 1.802775638 Reorder the terms: 1 + y = 1.802775638 Solving 1 + y = 1.802775638 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 = 1.802775638 + -1 Combine like terms: 1 + -1 = 0 0 + y = 1.802775638 + -1 y = 1.802775638 + -1 Combine like terms: 1.802775638 + -1 = 0.802775638 y = 0.802775638 Simplifying y = 0.802775638Subproblem 2
y + 1 = -1.802775638 Simplifying y + 1 = -1.802775638 Reorder the terms: 1 + y = -1.802775638 Solving 1 + y = -1.802775638 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 = -1.802775638 + -1 Combine like terms: 1 + -1 = 0 0 + y = -1.802775638 + -1 y = -1.802775638 + -1 Combine like terms: -1.802775638 + -1 = -2.802775638 y = -2.802775638 Simplifying y = -2.802775638Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.802775638, -2.802775638}
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