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Simplifying -5y2 + -26y + 160 = 0 Reorder the terms: 160 + -26y + -5y2 = 0 Solving 160 + -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'. -32 + 5.2y + y2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 5.2y + 32 + y2 = 0 + 32 Reorder the terms: -32 + 32 + 5.2y + y2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 5.2y + y2 = 0 + 32 5.2y + y2 = 0 + 32 Combine like terms: 0 + 32 = 32 5.2y + y2 = 32 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 = 32 + 6.76 Reorder the terms: 6.76 + 5.2y + y2 = 32 + 6.76 Combine like terms: 32 + 6.76 = 38.76 6.76 + 5.2y + y2 = 38.76 Factor a perfect square on the left side: (y + 2.6)(y + 2.6) = 38.76 Calculate the square root of the right side: 6.225752967 Break this problem into two subproblems by setting (y + 2.6) equal to 6.225752967 and -6.225752967.Subproblem 1
y + 2.6 = 6.225752967 Simplifying y + 2.6 = 6.225752967 Reorder the terms: 2.6 + y = 6.225752967 Solving 2.6 + y = 6.225752967 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 = 6.225752967 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + y = 6.225752967 + -2.6 y = 6.225752967 + -2.6 Combine like terms: 6.225752967 + -2.6 = 3.625752967 y = 3.625752967 Simplifying y = 3.625752967Subproblem 2
y + 2.6 = -6.225752967 Simplifying y + 2.6 = -6.225752967 Reorder the terms: 2.6 + y = -6.225752967 Solving 2.6 + y = -6.225752967 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 = -6.225752967 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + y = -6.225752967 + -2.6 y = -6.225752967 + -2.6 Combine like terms: -6.225752967 + -2.6 = -8.825752967 y = -8.825752967 Simplifying y = -8.825752967Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.625752967, -8.825752967}
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