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Simplifying 5y2 + -26y + 9 = 0 Reorder the terms: 9 + -26y + 5y2 = 0 Solving 9 + -26y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -5.2y + y2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -5.2y + -1.8 + y2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -5.2y + y2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -5.2y + y2 = 0 + -1.8 -5.2y + y2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -5.2y + y2 = -1.8 The y term is -5.2y. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2y + 6.76 + y2 = -1.8 + 6.76 Reorder the terms: 6.76 + -5.2y + y2 = -1.8 + 6.76 Combine like terms: -1.8 + 6.76 = 4.96 6.76 + -5.2y + y2 = 4.96 Factor a perfect square on the left side: (y + -2.6)(y + -2.6) = 4.96 Calculate the square root of the right side: 2.227105745 Break this problem into two subproblems by setting (y + -2.6) equal to 2.227105745 and -2.227105745.Subproblem 1
y + -2.6 = 2.227105745 Simplifying y + -2.6 = 2.227105745 Reorder the terms: -2.6 + y = 2.227105745 Solving -2.6 + y = 2.227105745 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + y = 2.227105745 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + y = 2.227105745 + 2.6 y = 2.227105745 + 2.6 Combine like terms: 2.227105745 + 2.6 = 4.827105745 y = 4.827105745 Simplifying y = 4.827105745Subproblem 2
y + -2.6 = -2.227105745 Simplifying y + -2.6 = -2.227105745 Reorder the terms: -2.6 + y = -2.227105745 Solving -2.6 + y = -2.227105745 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + y = -2.227105745 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + y = -2.227105745 + 2.6 y = -2.227105745 + 2.6 Combine like terms: -2.227105745 + 2.6 = 0.372894255 y = 0.372894255 Simplifying y = 0.372894255Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.827105745, 0.372894255}
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