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Simplifying 3y2 + -63y + 315 = 0 Reorder the terms: 315 + -63y + 3y2 = 0 Solving 315 + -63y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(105 + -21y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(105 + -21y + y2)' equal to zero and attempt to solve: Simplifying 105 + -21y + y2 = 0 Solving 105 + -21y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-105' to each side of the equation. 105 + -21y + -105 + y2 = 0 + -105 Reorder the terms: 105 + -105 + -21y + y2 = 0 + -105 Combine like terms: 105 + -105 = 0 0 + -21y + y2 = 0 + -105 -21y + y2 = 0 + -105 Combine like terms: 0 + -105 = -105 -21y + y2 = -105 The y term is -21y. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21y + 110.25 + y2 = -105 + 110.25 Reorder the terms: 110.25 + -21y + y2 = -105 + 110.25 Combine like terms: -105 + 110.25 = 5.25 110.25 + -21y + y2 = 5.25 Factor a perfect square on the left side: (y + -10.5)(y + -10.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (y + -10.5) equal to 2.291287847 and -2.291287847.Subproblem 1
y + -10.5 = 2.291287847 Simplifying y + -10.5 = 2.291287847 Reorder the terms: -10.5 + y = 2.291287847 Solving -10.5 + y = 2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = 2.291287847 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = 2.291287847 + 10.5 y = 2.291287847 + 10.5 Combine like terms: 2.291287847 + 10.5 = 12.791287847 y = 12.791287847 Simplifying y = 12.791287847Subproblem 2
y + -10.5 = -2.291287847 Simplifying y + -10.5 = -2.291287847 Reorder the terms: -10.5 + y = -2.291287847 Solving -10.5 + y = -2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = -2.291287847 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = -2.291287847 + 10.5 y = -2.291287847 + 10.5 Combine like terms: -2.291287847 + 10.5 = 8.208712153 y = 8.208712153 Simplifying y = 8.208712153Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.791287847, 8.208712153}Solution
y = {12.791287847, 8.208712153}
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