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Simplifying y = y2 + 625 + 4y + -100 + 15 Reorder the terms: y = 625 + -100 + 15 + 4y + y2 Combine like terms: 625 + -100 = 525 y = 525 + 15 + 4y + y2 Combine like terms: 525 + 15 = 540 y = 540 + 4y + y2 Solving y = 540 + 4y + y2 Solving for variable 'y'. Reorder the terms: -540 + y + -4y + -1y2 = 540 + 4y + y2 + -540 + -4y + -1y2 Combine like terms: y + -4y = -3y -540 + -3y + -1y2 = 540 + 4y + y2 + -540 + -4y + -1y2 Reorder the terms: -540 + -3y + -1y2 = 540 + -540 + 4y + -4y + y2 + -1y2 Combine like terms: 540 + -540 = 0 -540 + -3y + -1y2 = 0 + 4y + -4y + y2 + -1y2 -540 + -3y + -1y2 = 4y + -4y + y2 + -1y2 Combine like terms: 4y + -4y = 0 -540 + -3y + -1y2 = 0 + y2 + -1y2 -540 + -3y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -540 + -3y + -1y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(540 + 3y + y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(540 + 3y + y2)' equal to zero and attempt to solve: Simplifying 540 + 3y + y2 = 0 Solving 540 + 3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-540' to each side of the equation. 540 + 3y + -540 + y2 = 0 + -540 Reorder the terms: 540 + -540 + 3y + y2 = 0 + -540 Combine like terms: 540 + -540 = 0 0 + 3y + y2 = 0 + -540 3y + y2 = 0 + -540 Combine like terms: 0 + -540 = -540 3y + y2 = -540 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = -540 + 2.25 Reorder the terms: 2.25 + 3y + y2 = -540 + 2.25 Combine like terms: -540 + 2.25 = -537.75 2.25 + 3y + y2 = -537.75 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = -537.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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