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Simplifying -3y2 + -5y + 72 = 0 Reorder the terms: 72 + -5y + -3y2 = 0 Solving 72 + -5y + -3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -24 + 1.666666667y + y2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 1.666666667y + 24 + y2 = 0 + 24 Reorder the terms: -24 + 24 + 1.666666667y + y2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 1.666666667y + y2 = 0 + 24 1.666666667y + y2 = 0 + 24 Combine like terms: 0 + 24 = 24 1.666666667y + y2 = 24 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 = 24 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667y + y2 = 24 + 0.6944444447 Combine like terms: 24 + 0.6944444447 = 24.6944444447 0.6944444447 + 1.666666667y + y2 = 24.6944444447 Factor a perfect square on the left side: (y + 0.8333333335)(y + 0.8333333335) = 24.6944444447 Calculate the square root of the right side: 4.969350505 Break this problem into two subproblems by setting (y + 0.8333333335) equal to 4.969350505 and -4.969350505.Subproblem 1
y + 0.8333333335 = 4.969350505 Simplifying y + 0.8333333335 = 4.969350505 Reorder the terms: 0.8333333335 + y = 4.969350505 Solving 0.8333333335 + y = 4.969350505 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 = 4.969350505 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + y = 4.969350505 + -0.8333333335 y = 4.969350505 + -0.8333333335 Combine like terms: 4.969350505 + -0.8333333335 = 4.1360171715 y = 4.1360171715 Simplifying y = 4.1360171715Subproblem 2
y + 0.8333333335 = -4.969350505 Simplifying y + 0.8333333335 = -4.969350505 Reorder the terms: 0.8333333335 + y = -4.969350505 Solving 0.8333333335 + y = -4.969350505 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 = -4.969350505 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + y = -4.969350505 + -0.8333333335 y = -4.969350505 + -0.8333333335 Combine like terms: -4.969350505 + -0.8333333335 = -5.8026838385 y = -5.8026838385 Simplifying y = -5.8026838385Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.1360171715, -5.8026838385}
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