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Simplifying 100 + -20y = y2 Solving 100 + -20y = y2 Solving for variable 'y'. Combine like terms: y2 + -1y2 = 0 100 + -20y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + 20y + y2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 20y + 100 + y2 = 0 + 100 Reorder the terms: -100 + 100 + 20y + y2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 20y + y2 = 0 + 100 20y + y2 = 0 + 100 Combine like terms: 0 + 100 = 100 20y + y2 = 100 The y term is 20y. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20y + 100 + y2 = 100 + 100 Reorder the terms: 100 + 20y + y2 = 100 + 100 Combine like terms: 100 + 100 = 200 100 + 20y + y2 = 200 Factor a perfect square on the left side: (y + 10)(y + 10) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (y + 10) equal to 14.142135624 and -14.142135624.Subproblem 1
y + 10 = 14.142135624 Simplifying y + 10 = 14.142135624 Reorder the terms: 10 + y = 14.142135624 Solving 10 + y = 14.142135624 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + y = 14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + y = 14.142135624 + -10 y = 14.142135624 + -10 Combine like terms: 14.142135624 + -10 = 4.142135624 y = 4.142135624 Simplifying y = 4.142135624Subproblem 2
y + 10 = -14.142135624 Simplifying y + 10 = -14.142135624 Reorder the terms: 10 + y = -14.142135624 Solving 10 + y = -14.142135624 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + y = -14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + y = -14.142135624 + -10 y = -14.142135624 + -10 Combine like terms: -14.142135624 + -10 = -24.142135624 y = -24.142135624 Simplifying y = -24.142135624Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.142135624, -24.142135624}
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