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Simplifying 0 = y2 + 9y + 7 Reorder the terms: 0 = 7 + 9y + y2 Solving 0 = 7 + 9y + y2 Solving for variable 'y'. Combine like terms: 0 + -7 = -7 -7 + -9y + -1y2 = 7 + 9y + y2 + -7 + -9y + -1y2 Reorder the terms: -7 + -9y + -1y2 = 7 + -7 + 9y + -9y + y2 + -1y2 Combine like terms: 7 + -7 = 0 -7 + -9y + -1y2 = 0 + 9y + -9y + y2 + -1y2 -7 + -9y + -1y2 = 9y + -9y + y2 + -1y2 Combine like terms: 9y + -9y = 0 -7 + -9y + -1y2 = 0 + y2 + -1y2 -7 + -9y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -7 + -9y + -1y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 9y + y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 9y + y2)' equal to zero and attempt to solve: Simplifying 7 + 9y + y2 = 0 Solving 7 + 9y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 9y + -7 + y2 = 0 + -7 Reorder the terms: 7 + -7 + 9y + y2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9y + y2 = 0 + -7 9y + y2 = 0 + -7 Combine like terms: 0 + -7 = -7 9y + y2 = -7 The y term is 9y. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9y + 20.25 + y2 = -7 + 20.25 Reorder the terms: 20.25 + 9y + y2 = -7 + 20.25 Combine like terms: -7 + 20.25 = 13.25 20.25 + 9y + y2 = 13.25 Factor a perfect square on the left side: (y + 4.5)(y + 4.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (y + 4.5) equal to 3.640054945 and -3.640054945.Subproblem 1
y + 4.5 = 3.640054945 Simplifying y + 4.5 = 3.640054945 Reorder the terms: 4.5 + y = 3.640054945 Solving 4.5 + y = 3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = 3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 3.640054945 + -4.5 y = 3.640054945 + -4.5 Combine like terms: 3.640054945 + -4.5 = -0.859945055 y = -0.859945055 Simplifying y = -0.859945055Subproblem 2
y + 4.5 = -3.640054945 Simplifying y + 4.5 = -3.640054945 Reorder the terms: 4.5 + y = -3.640054945 Solving 4.5 + y = -3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = -3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -3.640054945 + -4.5 y = -3.640054945 + -4.5 Combine like terms: -3.640054945 + -4.5 = -8.140054945 y = -8.140054945 Simplifying y = -8.140054945Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.859945055, -8.140054945}Solution
y = {-0.859945055, -8.140054945}
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