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Simplifying 46y2 + 38y + 7 = 0 Reorder the terms: 7 + 38y + 46y2 = 0 Solving 7 + 38y + 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'. 0.152173913 + 0.8260869565y + y2 = 0 Move the constant term to the right: Add '-0.152173913' to each side of the equation. 0.152173913 + 0.8260869565y + -0.152173913 + y2 = 0 + -0.152173913 Reorder the terms: 0.152173913 + -0.152173913 + 0.8260869565y + y2 = 0 + -0.152173913 Combine like terms: 0.152173913 + -0.152173913 = 0.000000000 0.000000000 + 0.8260869565y + y2 = 0 + -0.152173913 0.8260869565y + y2 = 0 + -0.152173913 Combine like terms: 0 + -0.152173913 = -0.152173913 0.8260869565y + y2 = -0.152173913 The y term is 0.8260869565y. Take half its coefficient (0.4130434783). Square it (0.1706049150) and add it to both sides. Add '0.1706049150' to each side of the equation. 0.8260869565y + 0.1706049150 + y2 = -0.152173913 + 0.1706049150 Reorder the terms: 0.1706049150 + 0.8260869565y + y2 = -0.152173913 + 0.1706049150 Combine like terms: -0.152173913 + 0.1706049150 = 0.018431002 0.1706049150 + 0.8260869565y + y2 = 0.018431002 Factor a perfect square on the left side: (y + 0.4130434783)(y + 0.4130434783) = 0.018431002 Calculate the square root of the right side: 0.135760826 Break this problem into two subproblems by setting (y + 0.4130434783) equal to 0.135760826 and -0.135760826.Subproblem 1
y + 0.4130434783 = 0.135760826 Simplifying y + 0.4130434783 = 0.135760826 Reorder the terms: 0.4130434783 + y = 0.135760826 Solving 0.4130434783 + y = 0.135760826 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4130434783' to each side of the equation. 0.4130434783 + -0.4130434783 + y = 0.135760826 + -0.4130434783 Combine like terms: 0.4130434783 + -0.4130434783 = 0.0000000000 0.0000000000 + y = 0.135760826 + -0.4130434783 y = 0.135760826 + -0.4130434783 Combine like terms: 0.135760826 + -0.4130434783 = -0.2772826523 y = -0.2772826523 Simplifying y = -0.2772826523Subproblem 2
y + 0.4130434783 = -0.135760826 Simplifying y + 0.4130434783 = -0.135760826 Reorder the terms: 0.4130434783 + y = -0.135760826 Solving 0.4130434783 + y = -0.135760826 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4130434783' to each side of the equation. 0.4130434783 + -0.4130434783 + y = -0.135760826 + -0.4130434783 Combine like terms: 0.4130434783 + -0.4130434783 = 0.0000000000 0.0000000000 + y = -0.135760826 + -0.4130434783 y = -0.135760826 + -0.4130434783 Combine like terms: -0.135760826 + -0.4130434783 = -0.5488043043 y = -0.5488043043 Simplifying y = -0.5488043043Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.2772826523, -0.5488043043}
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