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Simplifying (y2 + 2y + 2) * 5 + y2 + 2y = 0 Reorder the terms: (2 + 2y + y2) * 5 + y2 + 2y = 0 Reorder the terms for easier multiplication: 5(2 + 2y + y2) + y2 + 2y = 0 (2 * 5 + 2y * 5 + y2 * 5) + y2 + 2y = 0 (10 + 10y + 5y2) + y2 + 2y = 0 Reorder the terms: 10 + 10y + 2y + 5y2 + y2 = 0 Combine like terms: 10y + 2y = 12y 10 + 12y + 5y2 + y2 = 0 Combine like terms: 5y2 + y2 = 6y2 10 + 12y + 6y2 = 0 Solving 10 + 12y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 6y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 6y + 3y2)' equal to zero and attempt to solve: Simplifying 5 + 6y + 3y2 = 0 Solving 5 + 6y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 2y + y2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 2y + -1.666666667 + y2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 2y + y2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 2y + y2 = 0 + -1.666666667 2y + y2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 2y + y2 = -1.666666667 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = -1.666666667 + 1 Reorder the terms: 1 + 2y + y2 = -1.666666667 + 1 Combine like terms: -1.666666667 + 1 = -0.666666667 1 + 2y + y2 = -0.666666667 Factor a perfect square on the left side: (y + 1)(y + 1) = -0.666666667 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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