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Simplifying y2 = 4y + 171 Reorder the terms: y2 = 171 + 4y Solving y2 = 171 + 4y Solving for variable 'y'. Reorder the terms: -171 + -4y + y2 = 171 + 4y + -171 + -4y Reorder the terms: -171 + -4y + y2 = 171 + -171 + 4y + -4y Combine like terms: 171 + -171 = 0 -171 + -4y + y2 = 0 + 4y + -4y -171 + -4y + y2 = 4y + -4y Combine like terms: 4y + -4y = 0 -171 + -4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '171' to each side of the equation. -171 + -4y + 171 + y2 = 0 + 171 Reorder the terms: -171 + 171 + -4y + y2 = 0 + 171 Combine like terms: -171 + 171 = 0 0 + -4y + y2 = 0 + 171 -4y + y2 = 0 + 171 Combine like terms: 0 + 171 = 171 -4y + y2 = 171 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 171 + 4 Reorder the terms: 4 + -4y + y2 = 171 + 4 Combine like terms: 171 + 4 = 175 4 + -4y + y2 = 175 Factor a perfect square on the left side: (y + -2)(y + -2) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (y + -2) equal to 13.228756555 and -13.228756555.Subproblem 1
y + -2 = 13.228756555 Simplifying y + -2 = 13.228756555 Reorder the terms: -2 + y = 13.228756555 Solving -2 + y = 13.228756555 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 13.228756555 + 2 Combine like terms: -2 + 2 = 0 0 + y = 13.228756555 + 2 y = 13.228756555 + 2 Combine like terms: 13.228756555 + 2 = 15.228756555 y = 15.228756555 Simplifying y = 15.228756555Subproblem 2
y + -2 = -13.228756555 Simplifying y + -2 = -13.228756555 Reorder the terms: -2 + y = -13.228756555 Solving -2 + y = -13.228756555 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -13.228756555 + 2 Combine like terms: -2 + 2 = 0 0 + y = -13.228756555 + 2 y = -13.228756555 + 2 Combine like terms: -13.228756555 + 2 = -11.228756555 y = -11.228756555 Simplifying y = -11.228756555Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.228756555, -11.228756555}
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