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Simplifying y2 + -7y + 12.25 = 0 Reorder the terms: 12.25 + -7y + y2 = 0 Solving 12.25 + -7y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + -7y + -12.25 + y2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + -7y + y2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + -7y + y2 = 0 + -12.25 -7y + y2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 -7y + y2 = -12.25 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = -12.25 + 12.25 Reorder the terms: 12.25 + -7y + y2 = -12.25 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 12.25 + -7y + y2 = 0.00 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (y + -3.5) equal to 0.00 and 0.00.Subproblem 1
y + -3.5 = 0.00 Simplifying y + -3.5 = 0.00 Reorder the terms: -3.5 + y = 0.00 Solving -3.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 0.00 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 0.00 + 3.5 y = 0.00 + 3.5 Combine like terms: 0.00 + 3.5 = 3.5 y = 3.5 Simplifying y = 3.5Subproblem 2
y + -3.5 = 0.00 Simplifying y + -3.5 = 0.00 Reorder the terms: -3.5 + y = 0.00 Solving -3.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 0.00 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 0.00 + 3.5 y = 0.00 + 3.5 Combine like terms: 0.00 + 3.5 = 3.5 y = 3.5 Simplifying y = 3.5Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.5, 3.5}
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