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Simplifying 11(y2 + -7y + 4) = 0 Reorder the terms: 11(4 + -7y + y2) = 0 (4 * 11 + -7y * 11 + y2 * 11) = 0 (44 + -77y + 11y2) = 0 Solving 44 + -77y + 11y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '11'. 11(4 + -7y + y2) = 0 Ignore the factor 11.Subproblem 1
Set the factor '(4 + -7y + y2)' equal to zero and attempt to solve: Simplifying 4 + -7y + y2 = 0 Solving 4 + -7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -7y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7y + y2 = 0 + -4 -7y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7y + y2 = -4 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = -4 + 12.25 Reorder the terms: 12.25 + -7y + y2 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + -7y + y2 = 8.25 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (y + -3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
y + -3.5 = 2.872281323 Simplifying y + -3.5 = 2.872281323 Reorder the terms: -3.5 + y = 2.872281323 Solving -3.5 + y = 2.872281323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 2.872281323 + 3.5 y = 2.872281323 + 3.5 Combine like terms: 2.872281323 + 3.5 = 6.372281323 y = 6.372281323 Simplifying y = 6.372281323Subproblem 2
y + -3.5 = -2.872281323 Simplifying y + -3.5 = -2.872281323 Reorder the terms: -3.5 + y = -2.872281323 Solving -3.5 + y = -2.872281323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -2.872281323 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -2.872281323 + 3.5 y = -2.872281323 + 3.5 Combine like terms: -2.872281323 + 3.5 = 0.627718677 y = 0.627718677 Simplifying y = 0.627718677Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.372281323, 0.627718677}Solution
y = {6.372281323, 0.627718677}
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