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Simplifying y2 + 30y + -25 = 100 Reorder the terms: -25 + 30y + y2 = 100 Solving -25 + 30y + y2 = 100 Solving for variable 'y'. Reorder the terms: -25 + -100 + 30y + y2 = 100 + -100 Combine like terms: -25 + -100 = -125 -125 + 30y + y2 = 100 + -100 Combine like terms: 100 + -100 = 0 -125 + 30y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 30y + 125 + y2 = 0 + 125 Reorder the terms: -125 + 125 + 30y + y2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 30y + y2 = 0 + 125 30y + y2 = 0 + 125 Combine like terms: 0 + 125 = 125 30y + y2 = 125 The y term is 30y. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30y + 225 + y2 = 125 + 225 Reorder the terms: 225 + 30y + y2 = 125 + 225 Combine like terms: 125 + 225 = 350 225 + 30y + y2 = 350 Factor a perfect square on the left side: (y + 15)(y + 15) = 350 Calculate the square root of the right side: 18.708286934 Break this problem into two subproblems by setting (y + 15) equal to 18.708286934 and -18.708286934.Subproblem 1
y + 15 = 18.708286934 Simplifying y + 15 = 18.708286934 Reorder the terms: 15 + y = 18.708286934 Solving 15 + y = 18.708286934 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + y = 18.708286934 + -15 Combine like terms: 15 + -15 = 0 0 + y = 18.708286934 + -15 y = 18.708286934 + -15 Combine like terms: 18.708286934 + -15 = 3.708286934 y = 3.708286934 Simplifying y = 3.708286934Subproblem 2
y + 15 = -18.708286934 Simplifying y + 15 = -18.708286934 Reorder the terms: 15 + y = -18.708286934 Solving 15 + y = -18.708286934 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + y = -18.708286934 + -15 Combine like terms: 15 + -15 = 0 0 + y = -18.708286934 + -15 y = -18.708286934 + -15 Combine like terms: -18.708286934 + -15 = -33.708286934 y = -33.708286934 Simplifying y = -33.708286934Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.708286934, -33.708286934}
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