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Simplifying (72 + -1y2) + y = 9 Remove parenthesis around (72 + -1y2) 72 + -1y2 + y = 9 Reorder the terms: 72 + y + -1y2 = 9 Solving 72 + y + -1y2 = 9 Solving for variable 'y'. Reorder the terms: 72 + -9 + y + -1y2 = 9 + -9 Combine like terms: 72 + -9 = 63 63 + y + -1y2 = 9 + -9 Combine like terms: 9 + -9 = 0 63 + y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + -1y + y2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + -1y + 63 + y2 = 0 + 63 Reorder the terms: -63 + 63 + -1y + y2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -1y + y2 = 0 + 63 -1y + y2 = 0 + 63 Combine like terms: 0 + 63 = 63 -1y + y2 = 63 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. -1y + 0.25 + y2 = 63 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 63 + 0.25 Combine like terms: 63 + 0.25 = 63.25 0.25 + -1y + y2 = 63.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (y + 0.5) equal to 7.95298686 and -7.95298686.Subproblem 1
y + 0.5 = 7.95298686 Simplifying y + 0.5 = 7.95298686 Reorder the terms: 0.5 + y = 7.95298686 Solving 0.5 + y = 7.95298686 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 = 7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 7.95298686 + -0.5 y = 7.95298686 + -0.5 Combine like terms: 7.95298686 + -0.5 = 7.45298686 y = 7.45298686 Simplifying y = 7.45298686Subproblem 2
y + 0.5 = -7.95298686 Simplifying y + 0.5 = -7.95298686 Reorder the terms: 0.5 + y = -7.95298686 Solving 0.5 + y = -7.95298686 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 = -7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -7.95298686 + -0.5 y = -7.95298686 + -0.5 Combine like terms: -7.95298686 + -0.5 = -8.45298686 y = -8.45298686 Simplifying y = -8.45298686Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.45298686, -8.45298686}
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