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Simplifying 0 = -1y2 + -70y + 1225 Reorder the terms: 0 = 1225 + -70y + -1y2 Solving 0 = 1225 + -70y + -1y2 Solving for variable 'y'. Combine like terms: 0 + -1225 = -1225 -1225 + 70y + y2 = 1225 + -70y + -1y2 + -1225 + 70y + y2 Reorder the terms: -1225 + 70y + y2 = 1225 + -1225 + -70y + 70y + -1y2 + y2 Combine like terms: 1225 + -1225 = 0 -1225 + 70y + y2 = 0 + -70y + 70y + -1y2 + y2 -1225 + 70y + y2 = -70y + 70y + -1y2 + y2 Combine like terms: -70y + 70y = 0 -1225 + 70y + y2 = 0 + -1y2 + y2 -1225 + 70y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 -1225 + 70y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '1225' to each side of the equation. -1225 + 70y + 1225 + y2 = 0 + 1225 Reorder the terms: -1225 + 1225 + 70y + y2 = 0 + 1225 Combine like terms: -1225 + 1225 = 0 0 + 70y + y2 = 0 + 1225 70y + y2 = 0 + 1225 Combine like terms: 0 + 1225 = 1225 70y + y2 = 1225 The y term is 70y. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70y + 1225 + y2 = 1225 + 1225 Reorder the terms: 1225 + 70y + y2 = 1225 + 1225 Combine like terms: 1225 + 1225 = 2450 1225 + 70y + y2 = 2450 Factor a perfect square on the left side: (y + 35)(y + 35) = 2450 Calculate the square root of the right side: 49.497474683 Break this problem into two subproblems by setting (y + 35) equal to 49.497474683 and -49.497474683.Subproblem 1
y + 35 = 49.497474683 Simplifying y + 35 = 49.497474683 Reorder the terms: 35 + y = 49.497474683 Solving 35 + y = 49.497474683 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + y = 49.497474683 + -35 Combine like terms: 35 + -35 = 0 0 + y = 49.497474683 + -35 y = 49.497474683 + -35 Combine like terms: 49.497474683 + -35 = 14.497474683 y = 14.497474683 Simplifying y = 14.497474683Subproblem 2
y + 35 = -49.497474683 Simplifying y + 35 = -49.497474683 Reorder the terms: 35 + y = -49.497474683 Solving 35 + y = -49.497474683 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + y = -49.497474683 + -35 Combine like terms: 35 + -35 = 0 0 + y = -49.497474683 + -35 y = -49.497474683 + -35 Combine like terms: -49.497474683 + -35 = -84.497474683 y = -84.497474683 Simplifying y = -84.497474683Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.497474683, -84.497474683}
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