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Simplifying 25 = y + y2 Solving 25 = y + y2 Solving for variable 'y'. Reorder the terms: 25 + -1y + -1y2 = y + -1y + y2 + -1y2 Combine like terms: y + -1y = 0 25 + -1y + -1y2 = 0 + y2 + -1y2 25 + -1y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 25 + -1y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + y + y2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + y + 25 + y2 = 0 + 25 Reorder the terms: -25 + 25 + y + y2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + y + y2 = 0 + 25 y + y2 = 0 + 25 Combine like terms: 0 + 25 = 25 y + y2 = 25 The y term is y. 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. + 0.25 + y2 = 25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = 25 + 0.25 Combine like terms: 25 + 0.25 = 25.25 1.25 + y2 = 25.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (y + 0.5) equal to 5.024937811 and -5.024937811.Subproblem 1
y + 0.5 = 5.024937811 Simplifying y + 0.5 = 5.024937811 Reorder the terms: 0.5 + y = 5.024937811 Solving 0.5 + y = 5.024937811 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 = 5.024937811 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 5.024937811 + -0.5 y = 5.024937811 + -0.5 Combine like terms: 5.024937811 + -0.5 = 4.524937811 y = 4.524937811 Simplifying y = 4.524937811Subproblem 2
y + 0.5 = -5.024937811 Simplifying y + 0.5 = -5.024937811 Reorder the terms: 0.5 + y = -5.024937811 Solving 0.5 + y = -5.024937811 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 = -5.024937811 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -5.024937811 + -0.5 y = -5.024937811 + -0.5 Combine like terms: -5.024937811 + -0.5 = -5.524937811 y = -5.524937811 Simplifying y = -5.524937811Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.524937811, -5.524937811}
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