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Simplifying 4y2 + -60y + 175 = 0 Reorder the terms: 175 + -60y + 4y2 = 0 Solving 175 + -60y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 43.75 + -15y + y2 = 0 Move the constant term to the right: Add '-43.75' to each side of the equation. 43.75 + -15y + -43.75 + y2 = 0 + -43.75 Reorder the terms: 43.75 + -43.75 + -15y + y2 = 0 + -43.75 Combine like terms: 43.75 + -43.75 = 0.00 0.00 + -15y + y2 = 0 + -43.75 -15y + y2 = 0 + -43.75 Combine like terms: 0 + -43.75 = -43.75 -15y + y2 = -43.75 The y term is -15y. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15y + 56.25 + y2 = -43.75 + 56.25 Reorder the terms: 56.25 + -15y + y2 = -43.75 + 56.25 Combine like terms: -43.75 + 56.25 = 12.5 56.25 + -15y + y2 = 12.5 Factor a perfect square on the left side: (y + -7.5)(y + -7.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (y + -7.5) equal to 3.535533906 and -3.535533906.Subproblem 1
y + -7.5 = 3.535533906 Simplifying y + -7.5 = 3.535533906 Reorder the terms: -7.5 + y = 3.535533906 Solving -7.5 + y = 3.535533906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = 3.535533906 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 3.535533906 + 7.5 y = 3.535533906 + 7.5 Combine like terms: 3.535533906 + 7.5 = 11.035533906 y = 11.035533906 Simplifying y = 11.035533906Subproblem 2
y + -7.5 = -3.535533906 Simplifying y + -7.5 = -3.535533906 Reorder the terms: -7.5 + y = -3.535533906 Solving -7.5 + y = -3.535533906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = -3.535533906 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -3.535533906 + 7.5 y = -3.535533906 + 7.5 Combine like terms: -3.535533906 + 7.5 = 3.964466094 y = 3.964466094 Simplifying y = 3.964466094Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.035533906, 3.964466094}
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