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Simplifying -7y + 46y2 + -14 + -10y = 0 Reorder the terms: -14 + -7y + -10y + 46y2 = 0 Combine like terms: -7y + -10y = -17y -14 + -17y + 46y2 = 0 Solving -14 + -17y + 46y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 46 the coefficient of the squared term: Divide each side by '46'. -0.3043478261 + -0.3695652174y + y2 = 0 Move the constant term to the right: Add '0.3043478261' to each side of the equation. -0.3043478261 + -0.3695652174y + 0.3043478261 + y2 = 0 + 0.3043478261 Reorder the terms: -0.3043478261 + 0.3043478261 + -0.3695652174y + y2 = 0 + 0.3043478261 Combine like terms: -0.3043478261 + 0.3043478261 = 0.0000000000 0.0000000000 + -0.3695652174y + y2 = 0 + 0.3043478261 -0.3695652174y + y2 = 0 + 0.3043478261 Combine like terms: 0 + 0.3043478261 = 0.3043478261 -0.3695652174y + y2 = 0.3043478261 The y term is -0.3695652174y. Take half its coefficient (-0.1847826087). Square it (0.03414461248) and add it to both sides. Add '0.03414461248' to each side of the equation. -0.3695652174y + 0.03414461248 + y2 = 0.3043478261 + 0.03414461248 Reorder the terms: 0.03414461248 + -0.3695652174y + y2 = 0.3043478261 + 0.03414461248 Combine like terms: 0.3043478261 + 0.03414461248 = 0.33849243858 0.03414461248 + -0.3695652174y + y2 = 0.33849243858 Factor a perfect square on the left side: (y + -0.1847826087)(y + -0.1847826087) = 0.33849243858 Calculate the square root of the right side: 0.58180103 Break this problem into two subproblems by setting (y + -0.1847826087) equal to 0.58180103 and -0.58180103.Subproblem 1
y + -0.1847826087 = 0.58180103 Simplifying y + -0.1847826087 = 0.58180103 Reorder the terms: -0.1847826087 + y = 0.58180103 Solving -0.1847826087 + y = 0.58180103 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1847826087' to each side of the equation. -0.1847826087 + 0.1847826087 + y = 0.58180103 + 0.1847826087 Combine like terms: -0.1847826087 + 0.1847826087 = 0.0000000000 0.0000000000 + y = 0.58180103 + 0.1847826087 y = 0.58180103 + 0.1847826087 Combine like terms: 0.58180103 + 0.1847826087 = 0.7665836387 y = 0.7665836387 Simplifying y = 0.7665836387Subproblem 2
y + -0.1847826087 = -0.58180103 Simplifying y + -0.1847826087 = -0.58180103 Reorder the terms: -0.1847826087 + y = -0.58180103 Solving -0.1847826087 + y = -0.58180103 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1847826087' to each side of the equation. -0.1847826087 + 0.1847826087 + y = -0.58180103 + 0.1847826087 Combine like terms: -0.1847826087 + 0.1847826087 = 0.0000000000 0.0000000000 + y = -0.58180103 + 0.1847826087 y = -0.58180103 + 0.1847826087 Combine like terms: -0.58180103 + 0.1847826087 = -0.3970184213 y = -0.3970184213 Simplifying y = -0.3970184213Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.7665836387, -0.3970184213}
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