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Simplifying 10y2 + -66y + 40 = 0 Reorder the terms: 40 + -66y + 10y2 = 0 Solving 40 + -66y + 10y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -33y + 5y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + -33y + 5y2)' equal to zero and attempt to solve: Simplifying 20 + -33y + 5y2 = 0 Solving 20 + -33y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + -6.6y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6.6y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -6.6y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6.6y + y2 = 0 + -4 -6.6y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6.6y + y2 = -4 The y term is -6.6y. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6y + 10.89 + y2 = -4 + 10.89 Reorder the terms: 10.89 + -6.6y + y2 = -4 + 10.89 Combine like terms: -4 + 10.89 = 6.89 10.89 + -6.6y + y2 = 6.89 Factor a perfect square on the left side: (y + -3.3)(y + -3.3) = 6.89 Calculate the square root of the right side: 2.62488095 Break this problem into two subproblems by setting (y + -3.3) equal to 2.62488095 and -2.62488095.Subproblem 1
y + -3.3 = 2.62488095 Simplifying y + -3.3 = 2.62488095 Reorder the terms: -3.3 + y = 2.62488095 Solving -3.3 + y = 2.62488095 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + y = 2.62488095 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + y = 2.62488095 + 3.3 y = 2.62488095 + 3.3 Combine like terms: 2.62488095 + 3.3 = 5.92488095 y = 5.92488095 Simplifying y = 5.92488095Subproblem 2
y + -3.3 = -2.62488095 Simplifying y + -3.3 = -2.62488095 Reorder the terms: -3.3 + y = -2.62488095 Solving -3.3 + y = -2.62488095 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + y = -2.62488095 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + y = -2.62488095 + 3.3 y = -2.62488095 + 3.3 Combine like terms: -2.62488095 + 3.3 = 0.67511905 y = 0.67511905 Simplifying y = 0.67511905Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.92488095, 0.67511905}Solution
y = {5.92488095, 0.67511905}
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