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Simplifying 5y2 + -32y + -2 = 0 Reorder the terms: -2 + -32y + 5y2 = 0 Solving -2 + -32y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -6.4y + y2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -6.4y + 0.4 + y2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -6.4y + y2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -6.4y + y2 = 0 + 0.4 -6.4y + y2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -6.4y + y2 = 0.4 The y term is -6.4y. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4y + 10.24 + y2 = 0.4 + 10.24 Reorder the terms: 10.24 + -6.4y + y2 = 0.4 + 10.24 Combine like terms: 0.4 + 10.24 = 10.64 10.24 + -6.4y + y2 = 10.64 Factor a perfect square on the left side: (y + -3.2)(y + -3.2) = 10.64 Calculate the square root of the right side: 3.261901286 Break this problem into two subproblems by setting (y + -3.2) equal to 3.261901286 and -3.261901286.Subproblem 1
y + -3.2 = 3.261901286 Simplifying y + -3.2 = 3.261901286 Reorder the terms: -3.2 + y = 3.261901286 Solving -3.2 + y = 3.261901286 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + y = 3.261901286 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + y = 3.261901286 + 3.2 y = 3.261901286 + 3.2 Combine like terms: 3.261901286 + 3.2 = 6.461901286 y = 6.461901286 Simplifying y = 6.461901286Subproblem 2
y + -3.2 = -3.261901286 Simplifying y + -3.2 = -3.261901286 Reorder the terms: -3.2 + y = -3.261901286 Solving -3.2 + y = -3.261901286 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + y = -3.261901286 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + y = -3.261901286 + 3.2 y = -3.261901286 + 3.2 Combine like terms: -3.261901286 + 3.2 = -0.061901286 y = -0.061901286 Simplifying y = -0.061901286Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.461901286, -0.061901286}
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