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Simplifying 2y2 + -20y + -7 = 0 Reorder the terms: -7 + -20y + 2y2 = 0 Solving -7 + -20y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -10y + y2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -10y + 3.5 + y2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -10y + y2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -10y + y2 = 0 + 3.5 -10y + y2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -10y + y2 = 3.5 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 3.5 + 25 Reorder the terms: 25 + -10y + y2 = 3.5 + 25 Combine like terms: 3.5 + 25 = 28.5 25 + -10y + y2 = 28.5 Factor a perfect square on the left side: (y + -5)(y + -5) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting (y + -5) equal to 5.338539126 and -5.338539126.Subproblem 1
y + -5 = 5.338539126 Simplifying y + -5 = 5.338539126 Reorder the terms: -5 + y = 5.338539126 Solving -5 + y = 5.338539126 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 5.338539126 + 5 Combine like terms: -5 + 5 = 0 0 + y = 5.338539126 + 5 y = 5.338539126 + 5 Combine like terms: 5.338539126 + 5 = 10.338539126 y = 10.338539126 Simplifying y = 10.338539126Subproblem 2
y + -5 = -5.338539126 Simplifying y + -5 = -5.338539126 Reorder the terms: -5 + y = -5.338539126 Solving -5 + y = -5.338539126 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -5.338539126 + 5 Combine like terms: -5 + 5 = 0 0 + y = -5.338539126 + 5 y = -5.338539126 + 5 Combine like terms: -5.338539126 + 5 = -0.338539126 y = -0.338539126 Simplifying y = -0.338539126Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.338539126, -0.338539126}
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