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Simplifying (-28y2) + (3y) + (287) = 0 (-28y2) + (3y) + 287 = 0 Reorder the terms: 287 + (3y) + (-28y2) = 0 Solving 287 + (3y) + (-28y2) = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -28 the coefficient of the squared term: Divide each side by '-28'. -10.25 + (-0.1071428571y) + y2 = 0 Move the constant term to the right: Add '10.25' to each side of the equation. -10.25 + (-0.1071428571y) + 10.25 + y2 = 0 + 10.25 Reorder the terms: -10.25 + 10.25 + (-0.1071428571y) + y2 = 0 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + (-0.1071428571y) + y2 = 0 + 10.25 (-0.1071428571y) + y2 = 0 + 10.25 Combine like terms: 0 + 10.25 = 10.25 (-0.1071428571y) + y2 = 10.25 The y term is (-0.1071428571y). Take half its coefficient (-0.05357142855). Square it (0.002869897957) and add it to both sides. Add '0.002869897957' to each side of the equation. (-0.1071428571y) + 0.002869897957 + y2 = 10.25 + 0.002869897957 Reorder the terms: 0.002869897957 + (-0.1071428571y) + y2 = 10.25 + 0.002869897957 Combine like terms: 10.25 + 0.002869897957 = 10.252869897957 0.002869897957 + (-0.1071428571y) + y2 = 10.252869897957 Factor a perfect square on the left side: ((y) + -0.05357142855)((y) + -0.05357142855) = 10.252869897957 Calculate the square root of the right side: 3.20201029 Break this problem into two subproblems by setting ((y) + -0.05357142855) equal to 3.20201029 and -3.20201029.Subproblem 1
(y) + -0.05357142855 = 3.20201029 Simplifying (y) + -0.05357142855 = 3.20201029 y + -0.05357142855 = 3.20201029 Reorder the terms: -0.05357142855 + y = 3.20201029 Solving -0.05357142855 + y = 3.20201029 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.05357142855' to each side of the equation. -0.05357142855 + 0.05357142855 + y = 3.20201029 + 0.05357142855 Combine like terms: -0.05357142855 + 0.05357142855 = 0.00000000000 0.00000000000 + y = 3.20201029 + 0.05357142855 y = 3.20201029 + 0.05357142855 Combine like terms: 3.20201029 + 0.05357142855 = 3.25558171855 y = 3.25558171855 Simplifying y = 3.25558171855Subproblem 2
(y) + -0.05357142855 = -3.20201029 Simplifying (y) + -0.05357142855 = -3.20201029 y + -0.05357142855 = -3.20201029 Reorder the terms: -0.05357142855 + y = -3.20201029 Solving -0.05357142855 + y = -3.20201029 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.05357142855' to each side of the equation. -0.05357142855 + 0.05357142855 + y = -3.20201029 + 0.05357142855 Combine like terms: -0.05357142855 + 0.05357142855 = 0.00000000000 0.00000000000 + y = -3.20201029 + 0.05357142855 y = -3.20201029 + 0.05357142855 Combine like terms: -3.20201029 + 0.05357142855 = -3.14843886145 y = -3.14843886145 Simplifying y = -3.14843886145Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.25558171855, -3.14843886145}
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