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Simplifying 7y2 + 30y + -3 = 0 Reorder the terms: -3 + 30y + 7y2 = 0 Solving -3 + 30y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 4.285714286y + y2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 4.285714286y + 0.4285714286 + y2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 4.285714286y + y2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 4.285714286y + y2 = 0 + 0.4285714286 4.285714286y + y2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 4.285714286y + y2 = 0.4285714286 The y term is 4.285714286y. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286y + 4.591836735 + y2 = 0.4285714286 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286y + y2 = 0.4285714286 + 4.591836735 Combine like terms: 0.4285714286 + 4.591836735 = 5.0204081636 4.591836735 + 4.285714286y + y2 = 5.0204081636 Factor a perfect square on the left side: (y + 2.142857143)(y + 2.142857143) = 5.0204081636 Calculate the square root of the right side: 2.240626735 Break this problem into two subproblems by setting (y + 2.142857143) equal to 2.240626735 and -2.240626735.Subproblem 1
y + 2.142857143 = 2.240626735 Simplifying y + 2.142857143 = 2.240626735 Reorder the terms: 2.142857143 + y = 2.240626735 Solving 2.142857143 + y = 2.240626735 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + y = 2.240626735 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + y = 2.240626735 + -2.142857143 y = 2.240626735 + -2.142857143 Combine like terms: 2.240626735 + -2.142857143 = 0.097769592 y = 0.097769592 Simplifying y = 0.097769592Subproblem 2
y + 2.142857143 = -2.240626735 Simplifying y + 2.142857143 = -2.240626735 Reorder the terms: 2.142857143 + y = -2.240626735 Solving 2.142857143 + y = -2.240626735 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + y = -2.240626735 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + y = -2.240626735 + -2.142857143 y = -2.240626735 + -2.142857143 Combine like terms: -2.240626735 + -2.142857143 = -4.383483878 y = -4.383483878 Simplifying y = -4.383483878Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.097769592, -4.383483878}
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