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Simplifying 8y2 + 14y = 5 Reorder the terms: 14y + 8y2 = 5 Solving 14y + 8y2 = 5 Solving for variable 'y'. Reorder the terms: -5 + 14y + 8y2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 14y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 1.75y + y2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 1.75y + 0.625 + y2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 1.75y + y2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 1.75y + y2 = 0 + 0.625 1.75y + y2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 1.75y + y2 = 0.625 The y term is 1.75y. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75y + 0.765625 + y2 = 0.625 + 0.765625 Reorder the terms: 0.765625 + 1.75y + y2 = 0.625 + 0.765625 Combine like terms: 0.625 + 0.765625 = 1.390625 0.765625 + 1.75y + y2 = 1.390625 Factor a perfect square on the left side: (y + 0.875)(y + 0.875) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (y + 0.875) equal to 1.179247642 and -1.179247642.Subproblem 1
y + 0.875 = 1.179247642 Simplifying y + 0.875 = 1.179247642 Reorder the terms: 0.875 + y = 1.179247642 Solving 0.875 + y = 1.179247642 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = 1.179247642 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = 1.179247642 + -0.875 y = 1.179247642 + -0.875 Combine like terms: 1.179247642 + -0.875 = 0.304247642 y = 0.304247642 Simplifying y = 0.304247642Subproblem 2
y + 0.875 = -1.179247642 Simplifying y + 0.875 = -1.179247642 Reorder the terms: 0.875 + y = -1.179247642 Solving 0.875 + y = -1.179247642 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = -1.179247642 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = -1.179247642 + -0.875 y = -1.179247642 + -0.875 Combine like terms: -1.179247642 + -0.875 = -2.054247642 y = -2.054247642 Simplifying y = -2.054247642Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.304247642, -2.054247642}
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