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Simplifying 10y2 + -150y + 525 = 0 Reorder the terms: 525 + -150y + 10y2 = 0 Solving 525 + -150y + 10y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(105 + -30y + 2y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(105 + -30y + 2y2)' equal to zero and attempt to solve: Simplifying 105 + -30y + 2y2 = 0 Solving 105 + -30y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 52.5 + -15y + y2 = 0 Move the constant term to the right: Add '-52.5' to each side of the equation. 52.5 + -15y + -52.5 + y2 = 0 + -52.5 Reorder the terms: 52.5 + -52.5 + -15y + y2 = 0 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + -15y + y2 = 0 + -52.5 -15y + y2 = 0 + -52.5 Combine like terms: 0 + -52.5 = -52.5 -15y + y2 = -52.5 The y term is -15y. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15y + 56.25 + y2 = -52.5 + 56.25 Reorder the terms: 56.25 + -15y + y2 = -52.5 + 56.25 Combine like terms: -52.5 + 56.25 = 3.75 56.25 + -15y + y2 = 3.75 Factor a perfect square on the left side: (y + -7.5)(y + -7.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (y + -7.5) equal to 1.936491673 and -1.936491673.Subproblem 1
y + -7.5 = 1.936491673 Simplifying y + -7.5 = 1.936491673 Reorder the terms: -7.5 + y = 1.936491673 Solving -7.5 + y = 1.936491673 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = 1.936491673 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 1.936491673 + 7.5 y = 1.936491673 + 7.5 Combine like terms: 1.936491673 + 7.5 = 9.436491673 y = 9.436491673 Simplifying y = 9.436491673Subproblem 2
y + -7.5 = -1.936491673 Simplifying y + -7.5 = -1.936491673 Reorder the terms: -7.5 + y = -1.936491673 Solving -7.5 + y = -1.936491673 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = -1.936491673 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -1.936491673 + 7.5 y = -1.936491673 + 7.5 Combine like terms: -1.936491673 + 7.5 = 5.563508327 y = 5.563508327 Simplifying y = 5.563508327Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.436491673, 5.563508327}Solution
y = {9.436491673, 5.563508327}
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