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Simplifying 2y2 + -210y + 105 = 0 Reorder the terms: 105 + -210y + 2y2 = 0 Solving 105 + -210y + 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'. 52.5 + -105y + y2 = 0 Move the constant term to the right: Add '-52.5' to each side of the equation. 52.5 + -105y + -52.5 + y2 = 0 + -52.5 Reorder the terms: 52.5 + -52.5 + -105y + y2 = 0 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + -105y + y2 = 0 + -52.5 -105y + y2 = 0 + -52.5 Combine like terms: 0 + -52.5 = -52.5 -105y + y2 = -52.5 The y term is -105y. Take half its coefficient (-52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. -105y + 2756.25 + y2 = -52.5 + 2756.25 Reorder the terms: 2756.25 + -105y + y2 = -52.5 + 2756.25 Combine like terms: -52.5 + 2756.25 = 2703.75 2756.25 + -105y + y2 = 2703.75 Factor a perfect square on the left side: (y + -52.5)(y + -52.5) = 2703.75 Calculate the square root of the right side: 51.997596098 Break this problem into two subproblems by setting (y + -52.5) equal to 51.997596098 and -51.997596098.Subproblem 1
y + -52.5 = 51.997596098 Simplifying y + -52.5 = 51.997596098 Reorder the terms: -52.5 + y = 51.997596098 Solving -52.5 + y = 51.997596098 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + y = 51.997596098 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + y = 51.997596098 + 52.5 y = 51.997596098 + 52.5 Combine like terms: 51.997596098 + 52.5 = 104.497596098 y = 104.497596098 Simplifying y = 104.497596098Subproblem 2
y + -52.5 = -51.997596098 Simplifying y + -52.5 = -51.997596098 Reorder the terms: -52.5 + y = -51.997596098 Solving -52.5 + y = -51.997596098 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + y = -51.997596098 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + y = -51.997596098 + 52.5 y = -51.997596098 + 52.5 Combine like terms: -51.997596098 + 52.5 = 0.502403902 y = 0.502403902 Simplifying y = 0.502403902Solution
The solution to the problem is based on the solutions from the subproblems. y = {104.497596098, 0.502403902}
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