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Simplifying 2 + -7y2 + -3y = 0 Reorder the terms: 2 + -3y + -7y2 = 0 Solving 2 + -3y + -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'. -0.2857142857 + 0.4285714286y + y2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.4285714286y + 0.2857142857 + y2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.4285714286y + y2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.4285714286y + y2 = 0 + 0.2857142857 0.4285714286y + y2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.4285714286y + y2 = 0.2857142857 The y term is 0.4285714286y. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286y + 0.04591836735 + y2 = 0.2857142857 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286y + y2 = 0.2857142857 + 0.04591836735 Combine like terms: 0.2857142857 + 0.04591836735 = 0.33163265305 0.04591836735 + 0.4285714286y + y2 = 0.33163265305 Factor a perfect square on the left side: (y + 0.2142857143)(y + 0.2142857143) = 0.33163265305 Calculate the square root of the right side: 0.575875553 Break this problem into two subproblems by setting (y + 0.2142857143) equal to 0.575875553 and -0.575875553.Subproblem 1
y + 0.2142857143 = 0.575875553 Simplifying y + 0.2142857143 = 0.575875553 Reorder the terms: 0.2142857143 + y = 0.575875553 Solving 0.2142857143 + y = 0.575875553 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + y = 0.575875553 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + y = 0.575875553 + -0.2142857143 y = 0.575875553 + -0.2142857143 Combine like terms: 0.575875553 + -0.2142857143 = 0.3615898387 y = 0.3615898387 Simplifying y = 0.3615898387Subproblem 2
y + 0.2142857143 = -0.575875553 Simplifying y + 0.2142857143 = -0.575875553 Reorder the terms: 0.2142857143 + y = -0.575875553 Solving 0.2142857143 + y = -0.575875553 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + y = -0.575875553 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + y = -0.575875553 + -0.2142857143 y = -0.575875553 + -0.2142857143 Combine like terms: -0.575875553 + -0.2142857143 = -0.7901612673 y = -0.7901612673 Simplifying y = -0.7901612673Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.3615898387, -0.7901612673}
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