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Simplifying 26y + -4y2 = 18 Solving 26y + -4y2 = 18 Solving for variable 'y'. Reorder the terms: -18 + 26y + -4y2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 26y + -4y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 13y + -2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 13y + -2y2)' equal to zero and attempt to solve: Simplifying -9 + 13y + -2y2 = 0 Solving -9 + 13y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 4.5 + -6.5y + y2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -6.5y + -4.5 + y2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -6.5y + y2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -6.5y + y2 = 0 + -4.5 -6.5y + y2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -6.5y + y2 = -4.5 The y term is -6.5y. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5y + 10.5625 + y2 = -4.5 + 10.5625 Reorder the terms: 10.5625 + -6.5y + y2 = -4.5 + 10.5625 Combine like terms: -4.5 + 10.5625 = 6.0625 10.5625 + -6.5y + y2 = 6.0625 Factor a perfect square on the left side: (y + -3.25)(y + -3.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (y + -3.25) equal to 2.46221445 and -2.46221445.Subproblem 1
y + -3.25 = 2.46221445 Simplifying y + -3.25 = 2.46221445 Reorder the terms: -3.25 + y = 2.46221445 Solving -3.25 + y = 2.46221445 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = 2.46221445 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = 2.46221445 + 3.25 y = 2.46221445 + 3.25 Combine like terms: 2.46221445 + 3.25 = 5.71221445 y = 5.71221445 Simplifying y = 5.71221445Subproblem 2
y + -3.25 = -2.46221445 Simplifying y + -3.25 = -2.46221445 Reorder the terms: -3.25 + y = -2.46221445 Solving -3.25 + y = -2.46221445 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = -2.46221445 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = -2.46221445 + 3.25 y = -2.46221445 + 3.25 Combine like terms: -2.46221445 + 3.25 = 0.78778555 y = 0.78778555 Simplifying y = 0.78778555Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.71221445, 0.78778555}Solution
y = {5.71221445, 0.78778555}
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