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Simplifying 4y + y2 + -247 = 0 Reorder the terms: -247 + 4y + y2 = 0 Solving -247 + 4y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '247' to each side of the equation. -247 + 4y + 247 + y2 = 0 + 247 Reorder the terms: -247 + 247 + 4y + y2 = 0 + 247 Combine like terms: -247 + 247 = 0 0 + 4y + y2 = 0 + 247 4y + y2 = 0 + 247 Combine like terms: 0 + 247 = 247 4y + y2 = 247 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 = 247 + 4 Reorder the terms: 4 + 4y + y2 = 247 + 4 Combine like terms: 247 + 4 = 251 4 + 4y + y2 = 251 Factor a perfect square on the left side: (y + 2)(y + 2) = 251 Calculate the square root of the right side: 15.842979518 Break this problem into two subproblems by setting (y + 2) equal to 15.842979518 and -15.842979518.Subproblem 1
y + 2 = 15.842979518 Simplifying y + 2 = 15.842979518 Reorder the terms: 2 + y = 15.842979518 Solving 2 + y = 15.842979518 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 = 15.842979518 + -2 Combine like terms: 2 + -2 = 0 0 + y = 15.842979518 + -2 y = 15.842979518 + -2 Combine like terms: 15.842979518 + -2 = 13.842979518 y = 13.842979518 Simplifying y = 13.842979518Subproblem 2
y + 2 = -15.842979518 Simplifying y + 2 = -15.842979518 Reorder the terms: 2 + y = -15.842979518 Solving 2 + y = -15.842979518 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 = -15.842979518 + -2 Combine like terms: 2 + -2 = 0 0 + y = -15.842979518 + -2 y = -15.842979518 + -2 Combine like terms: -15.842979518 + -2 = -17.842979518 y = -17.842979518 Simplifying y = -17.842979518Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.842979518, -17.842979518}
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