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Simplifying (y2 + -4y + 9) + -1(3y2 + -6y + -9) = 0 Reorder the terms: (9 + -4y + y2) + -1(3y2 + -6y + -9) = 0 Remove parenthesis around (9 + -4y + y2) 9 + -4y + y2 + -1(3y2 + -6y + -9) = 0 Reorder the terms: 9 + -4y + y2 + -1(-9 + -6y + 3y2) = 0 9 + -4y + y2 + (-9 * -1 + -6y * -1 + 3y2 * -1) = 0 9 + -4y + y2 + (9 + 6y + -3y2) = 0 Reorder the terms: 9 + 9 + -4y + 6y + y2 + -3y2 = 0 Combine like terms: 9 + 9 = 18 18 + -4y + 6y + y2 + -3y2 = 0 Combine like terms: -4y + 6y = 2y 18 + 2y + y2 + -3y2 = 0 Combine like terms: y2 + -3y2 = -2y2 18 + 2y + -2y2 = 0 Solving 18 + 2y + -2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + y + -1y2)' equal to zero and attempt to solve: Simplifying 9 + y + -1y2 = 0 Solving 9 + y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -1y + y2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -1y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -1y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1y + y2 = 0 + 9 -1y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1y + y2 = 9 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 = 9 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + -1y + y2 = 9.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (y + 0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
y + 0.5 = 3.041381265 Simplifying y + 0.5 = 3.041381265 Reorder the terms: 0.5 + y = 3.041381265 Solving 0.5 + y = 3.041381265 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 = 3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.041381265 + -0.5 y = 3.041381265 + -0.5 Combine like terms: 3.041381265 + -0.5 = 2.541381265 y = 2.541381265 Simplifying y = 2.541381265Subproblem 2
y + 0.5 = -3.041381265 Simplifying y + 0.5 = -3.041381265 Reorder the terms: 0.5 + y = -3.041381265 Solving 0.5 + y = -3.041381265 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 = -3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.041381265 + -0.5 y = -3.041381265 + -0.5 Combine like terms: -3.041381265 + -0.5 = -3.541381265 y = -3.541381265 Simplifying y = -3.541381265Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.541381265, -3.541381265}Solution
y = {2.541381265, -3.541381265}
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