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Simplifying 3y2 + 5y = 64 Reorder the terms: 5y + 3y2 = 64 Solving 5y + 3y2 = 64 Solving for variable 'y'. Reorder the terms: -64 + 5y + 3y2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 5y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21.33333333 + 1.666666667y + y2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + 1.666666667y + 21.33333333 + y2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + 1.666666667y + y2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + 1.666666667y + y2 = 0 + 21.33333333 1.666666667y + y2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 1.666666667y + y2 = 21.33333333 The y term is 1.666666667y. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667y + 0.6944444447 + y2 = 21.33333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667y + y2 = 21.33333333 + 0.6944444447 Combine like terms: 21.33333333 + 0.6944444447 = 22.0277777747 0.6944444447 + 1.666666667y + y2 = 22.0277777747 Factor a perfect square on the left side: (y + 0.8333333335)(y + 0.8333333335) = 22.0277777747 Calculate the square root of the right side: 4.693375946 Break this problem into two subproblems by setting (y + 0.8333333335) equal to 4.693375946 and -4.693375946.Subproblem 1
y + 0.8333333335 = 4.693375946 Simplifying y + 0.8333333335 = 4.693375946 Reorder the terms: 0.8333333335 + y = 4.693375946 Solving 0.8333333335 + y = 4.693375946 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + y = 4.693375946 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + y = 4.693375946 + -0.8333333335 y = 4.693375946 + -0.8333333335 Combine like terms: 4.693375946 + -0.8333333335 = 3.8600426125 y = 3.8600426125 Simplifying y = 3.8600426125Subproblem 2
y + 0.8333333335 = -4.693375946 Simplifying y + 0.8333333335 = -4.693375946 Reorder the terms: 0.8333333335 + y = -4.693375946 Solving 0.8333333335 + y = -4.693375946 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + y = -4.693375946 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + y = -4.693375946 + -0.8333333335 y = -4.693375946 + -0.8333333335 Combine like terms: -4.693375946 + -0.8333333335 = -5.5267092795 y = -5.5267092795 Simplifying y = -5.5267092795Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.8600426125, -5.5267092795}
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