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Simplifying 4y2 + 11y + 7 = 5 Reorder the terms: 7 + 11y + 4y2 = 5 Solving 7 + 11y + 4y2 = 5 Solving for variable 'y'. Reorder the terms: 7 + -5 + 11y + 4y2 = 5 + -5 Combine like terms: 7 + -5 = 2 2 + 11y + 4y2 = 5 + -5 Combine like terms: 5 + -5 = 0 2 + 11y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 2.75y + y2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 2.75y + -0.5 + y2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 2.75y + y2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 2.75y + y2 = 0 + -0.5 2.75y + y2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 2.75y + y2 = -0.5 The y term is 2.75y. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75y + 1.890625 + y2 = -0.5 + 1.890625 Reorder the terms: 1.890625 + 2.75y + y2 = -0.5 + 1.890625 Combine like terms: -0.5 + 1.890625 = 1.390625 1.890625 + 2.75y + y2 = 1.390625 Factor a perfect square on the left side: (y + 1.375)(y + 1.375) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (y + 1.375) equal to 1.179247642 and -1.179247642.Subproblem 1
y + 1.375 = 1.179247642 Simplifying y + 1.375 = 1.179247642 Reorder the terms: 1.375 + y = 1.179247642 Solving 1.375 + y = 1.179247642 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + y = 1.179247642 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + y = 1.179247642 + -1.375 y = 1.179247642 + -1.375 Combine like terms: 1.179247642 + -1.375 = -0.195752358 y = -0.195752358 Simplifying y = -0.195752358Subproblem 2
y + 1.375 = -1.179247642 Simplifying y + 1.375 = -1.179247642 Reorder the terms: 1.375 + y = -1.179247642 Solving 1.375 + y = -1.179247642 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + y = -1.179247642 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + y = -1.179247642 + -1.375 y = -1.179247642 + -1.375 Combine like terms: -1.179247642 + -1.375 = -2.554247642 y = -2.554247642 Simplifying y = -2.554247642Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.195752358, -2.554247642}
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