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Simplifying y2 + -17y + -70 = 0 Reorder the terms: -70 + -17y + y2 = 0 Solving -70 + -17y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -17y + 70 + y2 = 0 + 70 Reorder the terms: -70 + 70 + -17y + y2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -17y + y2 = 0 + 70 -17y + y2 = 0 + 70 Combine like terms: 0 + 70 = 70 -17y + y2 = 70 The y term is -17y. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17y + 72.25 + y2 = 70 + 72.25 Reorder the terms: 72.25 + -17y + y2 = 70 + 72.25 Combine like terms: 70 + 72.25 = 142.25 72.25 + -17y + y2 = 142.25 Factor a perfect square on the left side: (y + -8.5)(y + -8.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (y + -8.5) equal to 11.926860442 and -11.926860442.Subproblem 1
y + -8.5 = 11.926860442 Simplifying y + -8.5 = 11.926860442 Reorder the terms: -8.5 + y = 11.926860442 Solving -8.5 + y = 11.926860442 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = 11.926860442 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = 11.926860442 + 8.5 y = 11.926860442 + 8.5 Combine like terms: 11.926860442 + 8.5 = 20.426860442 y = 20.426860442 Simplifying y = 20.426860442Subproblem 2
y + -8.5 = -11.926860442 Simplifying y + -8.5 = -11.926860442 Reorder the terms: -8.5 + y = -11.926860442 Solving -8.5 + y = -11.926860442 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = -11.926860442 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = -11.926860442 + 8.5 y = -11.926860442 + 8.5 Combine like terms: -11.926860442 + 8.5 = -3.426860442 y = -3.426860442 Simplifying y = -3.426860442Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.426860442, -3.426860442}
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