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Simplifying 4y2 + -96y + 125 = 0 Reorder the terms: 125 + -96y + 4y2 = 0 Solving 125 + -96y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 31.25 + -24y + y2 = 0 Move the constant term to the right: Add '-31.25' to each side of the equation. 31.25 + -24y + -31.25 + y2 = 0 + -31.25 Reorder the terms: 31.25 + -31.25 + -24y + y2 = 0 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + -24y + y2 = 0 + -31.25 -24y + y2 = 0 + -31.25 Combine like terms: 0 + -31.25 = -31.25 -24y + y2 = -31.25 The y term is -24y. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24y + 144 + y2 = -31.25 + 144 Reorder the terms: 144 + -24y + y2 = -31.25 + 144 Combine like terms: -31.25 + 144 = 112.75 144 + -24y + y2 = 112.75 Factor a perfect square on the left side: (y + -12)(y + -12) = 112.75 Calculate the square root of the right side: 10.618380291 Break this problem into two subproblems by setting (y + -12) equal to 10.618380291 and -10.618380291.Subproblem 1
y + -12 = 10.618380291 Simplifying y + -12 = 10.618380291 Reorder the terms: -12 + y = 10.618380291 Solving -12 + y = 10.618380291 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = 10.618380291 + 12 Combine like terms: -12 + 12 = 0 0 + y = 10.618380291 + 12 y = 10.618380291 + 12 Combine like terms: 10.618380291 + 12 = 22.618380291 y = 22.618380291 Simplifying y = 22.618380291Subproblem 2
y + -12 = -10.618380291 Simplifying y + -12 = -10.618380291 Reorder the terms: -12 + y = -10.618380291 Solving -12 + y = -10.618380291 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = -10.618380291 + 12 Combine like terms: -12 + 12 = 0 0 + y = -10.618380291 + 12 y = -10.618380291 + 12 Combine like terms: -10.618380291 + 12 = 1.381619709 y = 1.381619709 Simplifying y = 1.381619709Solution
The solution to the problem is based on the solutions from the subproblems. y = {22.618380291, 1.381619709}
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