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Simplifying -4y2 + 34y + 24 = 0 Reorder the terms: 24 + 34y + -4y2 = 0 Solving 24 + 34y + -4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 17y + -2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 17y + -2y2)' equal to zero and attempt to solve: Simplifying 12 + 17y + -2y2 = 0 Solving 12 + 17y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6 + -8.5y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -8.5y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -8.5y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -8.5y + y2 = 0 + 6 -8.5y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -8.5y + y2 = 6 The y term is -8.5y. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5y + 18.0625 + y2 = 6 + 18.0625 Reorder the terms: 18.0625 + -8.5y + y2 = 6 + 18.0625 Combine like terms: 6 + 18.0625 = 24.0625 18.0625 + -8.5y + y2 = 24.0625 Factor a perfect square on the left side: (y + -4.25)(y + -4.25) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (y + -4.25) equal to 4.905354218 and -4.905354218.Subproblem 1
y + -4.25 = 4.905354218 Simplifying y + -4.25 = 4.905354218 Reorder the terms: -4.25 + y = 4.905354218 Solving -4.25 + y = 4.905354218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + y = 4.905354218 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + y = 4.905354218 + 4.25 y = 4.905354218 + 4.25 Combine like terms: 4.905354218 + 4.25 = 9.155354218 y = 9.155354218 Simplifying y = 9.155354218Subproblem 2
y + -4.25 = -4.905354218 Simplifying y + -4.25 = -4.905354218 Reorder the terms: -4.25 + y = -4.905354218 Solving -4.25 + y = -4.905354218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + y = -4.905354218 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + y = -4.905354218 + 4.25 y = -4.905354218 + 4.25 Combine like terms: -4.905354218 + 4.25 = -0.655354218 y = -0.655354218 Simplifying y = -0.655354218Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.155354218, -0.655354218}Solution
y = {9.155354218, -0.655354218}
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