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Simplifying 5 + -2y[8 + -1(4y + -3) + 14y] = 15y + -1[-8 + (2y + -5) + 11y] Reorder the terms: 5 + -2y[8 + -1(-3 + 4y) + 14y] = 15y + -1[-8 + (2y + -5) + 11y] 5 + -2y[8 + (-3 * -1 + 4y * -1) + 14y] = 15y + -1[-8 + (2y + -5) + 11y] 5 + -2y[8 + (3 + -4y) + 14y] = 15y + -1[-8 + (2y + -5) + 11y] Combine like terms: 8 + 3 = 11 5 + -2y[11 + -4y + 14y] = 15y + -1[-8 + (2y + -5) + 11y] Combine like terms: -4y + 14y = 10y 5 + -2y[11 + 10y] = 15y + -1[-8 + (2y + -5) + 11y] 5 + [11 * -2y + 10y * -2y] = 15y + -1[-8 + (2y + -5) + 11y] 5 + [-22y + -20y2] = 15y + -1[-8 + (2y + -5) + 11y] Reorder the terms: 5 + -22y + -20y2 = 15y + -1[-8 + (-5 + 2y) + 11y] Remove parenthesis around (-5 + 2y) 5 + -22y + -20y2 = 15y + -1[-8 + -5 + 2y + 11y] Combine like terms: -8 + -5 = -13 5 + -22y + -20y2 = 15y + -1[-13 + 2y + 11y] Combine like terms: 2y + 11y = 13y 5 + -22y + -20y2 = 15y + -1[-13 + 13y] 5 + -22y + -20y2 = 15y + [-13 * -1 + 13y * -1] 5 + -22y + -20y2 = 15y + [13 + -13y] Reorder the terms: 5 + -22y + -20y2 = 13 + 15y + -13y Combine like terms: 15y + -13y = 2y 5 + -22y + -20y2 = 13 + 2y Solving 5 + -22y + -20y2 = 13 + 2y Solving for variable 'y'. Reorder the terms: 5 + -13 + -22y + -2y + -20y2 = 13 + 2y + -13 + -2y Combine like terms: 5 + -13 = -8 -8 + -22y + -2y + -20y2 = 13 + 2y + -13 + -2y Combine like terms: -22y + -2y = -24y -8 + -24y + -20y2 = 13 + 2y + -13 + -2y Reorder the terms: -8 + -24y + -20y2 = 13 + -13 + 2y + -2y Combine like terms: 13 + -13 = 0 -8 + -24y + -20y2 = 0 + 2y + -2y -8 + -24y + -20y2 = 2y + -2y Combine like terms: 2y + -2y = 0 -8 + -24y + -20y2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(2 + 6y + 5y2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(2 + 6y + 5y2)' equal to zero and attempt to solve: Simplifying 2 + 6y + 5y2 = 0 Solving 2 + 6y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 1.2y + y2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.2y + -0.4 + y2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.2y + y2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.2y + y2 = 0 + -0.4 1.2y + y2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.2y + y2 = -0.4 The y term is 1.2y. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2y + 0.36 + y2 = -0.4 + 0.36 Reorder the terms: 0.36 + 1.2y + y2 = -0.4 + 0.36 Combine like terms: -0.4 + 0.36 = -0.04 0.36 + 1.2y + y2 = -0.04 Factor a perfect square on the left side: (y + 0.6)(y + 0.6) = -0.04 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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