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Simplifying -5(6y + -6) + -1y = -3y(y + -5) Reorder the terms: -5(-6 + 6y) + -1y = -3y(y + -5) (-6 * -5 + 6y * -5) + -1y = -3y(y + -5) (30 + -30y) + -1y = -3y(y + -5) Combine like terms: -30y + -1y = -31y 30 + -31y = -3y(y + -5) Reorder the terms: 30 + -31y = -3y(-5 + y) 30 + -31y = (-5 * -3y + y * -3y) 30 + -31y = (15y + -3y2) Solving 30 + -31y = 15y + -3y2 Solving for variable 'y'. Combine like terms: -31y + -15y = -46y 30 + -46y + 3y2 = 15y + -3y2 + -15y + 3y2 Reorder the terms: 30 + -46y + 3y2 = 15y + -15y + -3y2 + 3y2 Combine like terms: 15y + -15y = 0 30 + -46y + 3y2 = 0 + -3y2 + 3y2 30 + -46y + 3y2 = -3y2 + 3y2 Combine like terms: -3y2 + 3y2 = 0 30 + -46y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + -15.33333333y + y2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -15.33333333y + -10 + y2 = 0 + -10 Reorder the terms: 10 + -10 + -15.33333333y + y2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -15.33333333y + y2 = 0 + -10 -15.33333333y + y2 = 0 + -10 Combine like terms: 0 + -10 = -10 -15.33333333y + y2 = -10 The y term is -15.33333333y. Take half its coefficient (-7.666666665). Square it (58.77777775) and add it to both sides. Add '58.77777775' to each side of the equation. -15.33333333y + 58.77777775 + y2 = -10 + 58.77777775 Reorder the terms: 58.77777775 + -15.33333333y + y2 = -10 + 58.77777775 Combine like terms: -10 + 58.77777775 = 48.77777775 58.77777775 + -15.33333333y + y2 = 48.77777775 Factor a perfect square on the left side: (y + -7.666666665)(y + -7.666666665) = 48.77777775 Calculate the square root of the right side: 6.984108945 Break this problem into two subproblems by setting (y + -7.666666665) equal to 6.984108945 and -6.984108945.Subproblem 1
y + -7.666666665 = 6.984108945 Simplifying y + -7.666666665 = 6.984108945 Reorder the terms: -7.666666665 + y = 6.984108945 Solving -7.666666665 + y = 6.984108945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.666666665' to each side of the equation. -7.666666665 + 7.666666665 + y = 6.984108945 + 7.666666665 Combine like terms: -7.666666665 + 7.666666665 = 0.000000000 0.000000000 + y = 6.984108945 + 7.666666665 y = 6.984108945 + 7.666666665 Combine like terms: 6.984108945 + 7.666666665 = 14.65077561 y = 14.65077561 Simplifying y = 14.65077561Subproblem 2
y + -7.666666665 = -6.984108945 Simplifying y + -7.666666665 = -6.984108945 Reorder the terms: -7.666666665 + y = -6.984108945 Solving -7.666666665 + y = -6.984108945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.666666665' to each side of the equation. -7.666666665 + 7.666666665 + y = -6.984108945 + 7.666666665 Combine like terms: -7.666666665 + 7.666666665 = 0.000000000 0.000000000 + y = -6.984108945 + 7.666666665 y = -6.984108945 + 7.666666665 Combine like terms: -6.984108945 + 7.666666665 = 0.68255772 y = 0.68255772 Simplifying y = 0.68255772Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.65077561, 0.68255772}
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