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Simplifying 65 = 25 + -10y + y2 Solving 65 = 25 + -10y + y2 Solving for variable 'y'. Combine like terms: 65 + -25 = 40 40 + 10y + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2 Reorder the terms: 40 + 10y + -1y2 = 25 + -25 + -10y + 10y + y2 + -1y2 Combine like terms: 25 + -25 = 0 40 + 10y + -1y2 = 0 + -10y + 10y + y2 + -1y2 40 + 10y + -1y2 = -10y + 10y + y2 + -1y2 Combine like terms: -10y + 10y = 0 40 + 10y + -1y2 = 0 + y2 + -1y2 40 + 10y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 40 + 10y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + -10y + y2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -10y + 40 + y2 = 0 + 40 Reorder the terms: -40 + 40 + -10y + y2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -10y + y2 = 0 + 40 -10y + y2 = 0 + 40 Combine like terms: 0 + 40 = 40 -10y + y2 = 40 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 40 + 25 Reorder the terms: 25 + -10y + y2 = 40 + 25 Combine like terms: 40 + 25 = 65 25 + -10y + y2 = 65 Factor a perfect square on the left side: (y + -5)(y + -5) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (y + -5) equal to 8.062257748 and -8.062257748.Subproblem 1
y + -5 = 8.062257748 Simplifying y + -5 = 8.062257748 Reorder the terms: -5 + y = 8.062257748 Solving -5 + y = 8.062257748 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 8.062257748 + 5 Combine like terms: -5 + 5 = 0 0 + y = 8.062257748 + 5 y = 8.062257748 + 5 Combine like terms: 8.062257748 + 5 = 13.062257748 y = 13.062257748 Simplifying y = 13.062257748Subproblem 2
y + -5 = -8.062257748 Simplifying y + -5 = -8.062257748 Reorder the terms: -5 + y = -8.062257748 Solving -5 + y = -8.062257748 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -8.062257748 + 5 Combine like terms: -5 + 5 = 0 0 + y = -8.062257748 + 5 y = -8.062257748 + 5 Combine like terms: -8.062257748 + 5 = -3.062257748 y = -3.062257748 Simplifying y = -3.062257748Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.062257748, -3.062257748}
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