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Simplifying 5y2 + -7y + -32 = 0 Reorder the terms: -32 + -7y + 5y2 = 0 Solving -32 + -7y + 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'. -6.4 + -1.4y + y2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + -1.4y + 6.4 + y2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + -1.4y + y2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + -1.4y + y2 = 0 + 6.4 -1.4y + y2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 -1.4y + y2 = 6.4 The y term is -1.4y. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4y + 0.49 + y2 = 6.4 + 0.49 Reorder the terms: 0.49 + -1.4y + y2 = 6.4 + 0.49 Combine like terms: 6.4 + 0.49 = 6.89 0.49 + -1.4y + y2 = 6.89 Factor a perfect square on the left side: (y + -0.7)(y + -0.7) = 6.89 Calculate the square root of the right side: 2.62488095 Break this problem into two subproblems by setting (y + -0.7) equal to 2.62488095 and -2.62488095.Subproblem 1
y + -0.7 = 2.62488095 Simplifying y + -0.7 = 2.62488095 Reorder the terms: -0.7 + y = 2.62488095 Solving -0.7 + y = 2.62488095 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + y = 2.62488095 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + y = 2.62488095 + 0.7 y = 2.62488095 + 0.7 Combine like terms: 2.62488095 + 0.7 = 3.32488095 y = 3.32488095 Simplifying y = 3.32488095Subproblem 2
y + -0.7 = -2.62488095 Simplifying y + -0.7 = -2.62488095 Reorder the terms: -0.7 + y = -2.62488095 Solving -0.7 + y = -2.62488095 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + y = -2.62488095 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + y = -2.62488095 + 0.7 y = -2.62488095 + 0.7 Combine like terms: -2.62488095 + 0.7 = -1.92488095 y = -1.92488095 Simplifying y = -1.92488095Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.32488095, -1.92488095}
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