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Simplifying y2 = y + 100 Reorder the terms: y2 = 100 + y Solving y2 = 100 + y Solving for variable 'y'. Reorder the terms: -100 + -1y + y2 = 100 + y + -100 + -1y Reorder the terms: -100 + -1y + y2 = 100 + -100 + y + -1y Combine like terms: 100 + -100 = 0 -100 + -1y + y2 = 0 + y + -1y -100 + -1y + y2 = y + -1y Combine like terms: y + -1y = 0 -100 + -1y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -1y + 100 + y2 = 0 + 100 Reorder the terms: -100 + 100 + -1y + y2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -1y + y2 = 0 + 100 -1y + y2 = 0 + 100 Combine like terms: 0 + 100 = 100 -1y + y2 = 100 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 100 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 100 + 0.25 Combine like terms: 100 + 0.25 = 100.25 0.25 + -1y + y2 = 100.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (y + -0.5) equal to 10.012492197 and -10.012492197.Subproblem 1
y + -0.5 = 10.012492197 Simplifying y + -0.5 = 10.012492197 Reorder the terms: -0.5 + y = 10.012492197 Solving -0.5 + y = 10.012492197 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 10.012492197 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 10.012492197 + 0.5 y = 10.012492197 + 0.5 Combine like terms: 10.012492197 + 0.5 = 10.512492197 y = 10.512492197 Simplifying y = 10.512492197Subproblem 2
y + -0.5 = -10.012492197 Simplifying y + -0.5 = -10.012492197 Reorder the terms: -0.5 + y = -10.012492197 Solving -0.5 + y = -10.012492197 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -10.012492197 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -10.012492197 + 0.5 y = -10.012492197 + 0.5 Combine like terms: -10.012492197 + 0.5 = -9.512492197 y = -9.512492197 Simplifying y = -9.512492197Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.512492197, -9.512492197}
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