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Simplifying (-9y2 + -9y) + (8y2 + 2y + -7) = 0 Reorder the terms: (-9y + -9y2) + (8y2 + 2y + -7) = 0 Remove parenthesis around (-9y + -9y2) -9y + -9y2 + (8y2 + 2y + -7) = 0 Reorder the terms: -9y + -9y2 + (-7 + 2y + 8y2) = 0 Remove parenthesis around (-7 + 2y + 8y2) -9y + -9y2 + -7 + 2y + 8y2 = 0 Reorder the terms: -7 + -9y + 2y + -9y2 + 8y2 = 0 Combine like terms: -9y + 2y = -7y -7 + -7y + -9y2 + 8y2 = 0 Combine like terms: -9y2 + 8y2 = -1y2 -7 + -7y + -1y2 = 0 Solving -7 + -7y + -1y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 7y + y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 7y + y2)' equal to zero and attempt to solve: Simplifying 7 + 7y + y2 = 0 Solving 7 + 7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 7y + -7 + y2 = 0 + -7 Reorder the terms: 7 + -7 + 7y + y2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 7y + y2 = 0 + -7 7y + y2 = 0 + -7 Combine like terms: 0 + -7 = -7 7y + y2 = -7 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = -7 + 12.25 Reorder the terms: 12.25 + 7y + y2 = -7 + 12.25 Combine like terms: -7 + 12.25 = 5.25 12.25 + 7y + y2 = 5.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (y + 3.5) equal to 2.291287847 and -2.291287847.Subproblem 1
y + 3.5 = 2.291287847 Simplifying y + 3.5 = 2.291287847 Reorder the terms: 3.5 + y = 2.291287847 Solving 3.5 + y = 2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 2.291287847 + -3.5 y = 2.291287847 + -3.5 Combine like terms: 2.291287847 + -3.5 = -1.208712153 y = -1.208712153 Simplifying y = -1.208712153Subproblem 2
y + 3.5 = -2.291287847 Simplifying y + 3.5 = -2.291287847 Reorder the terms: 3.5 + y = -2.291287847 Solving 3.5 + y = -2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -2.291287847 + -3.5 y = -2.291287847 + -3.5 Combine like terms: -2.291287847 + -3.5 = -5.791287847 y = -5.791287847 Simplifying y = -5.791287847Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.208712153, -5.791287847}Solution
y = {-1.208712153, -5.791287847}
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