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Simplifying 10(2y + 2) * 2y = 2(8y + -8) Reorder the terms: 10(2 + 2y) * 2y = 2(8y + -8) Reorder the terms for easier multiplication: 10 * 2y(2 + 2y) = 2(8y + -8) Multiply 10 * 2 20y(2 + 2y) = 2(8y + -8) (2 * 20y + 2y * 20y) = 2(8y + -8) (40y + 40y2) = 2(8y + -8) Reorder the terms: 40y + 40y2 = 2(-8 + 8y) 40y + 40y2 = (-8 * 2 + 8y * 2) 40y + 40y2 = (-16 + 16y) Solving 40y + 40y2 = -16 + 16y Solving for variable 'y'. Reorder the terms: 16 + 40y + -16y + 40y2 = -16 + 16y + 16 + -16y Combine like terms: 40y + -16y = 24y 16 + 24y + 40y2 = -16 + 16y + 16 + -16y Reorder the terms: 16 + 24y + 40y2 = -16 + 16 + 16y + -16y Combine like terms: -16 + 16 = 0 16 + 24y + 40y2 = 0 + 16y + -16y 16 + 24y + 40y2 = 16y + -16y Combine like terms: 16y + -16y = 0 16 + 24y + 40y2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(2 + 3y + 5y2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(2 + 3y + 5y2)' equal to zero and attempt to solve: Simplifying 2 + 3y + 5y2 = 0 Solving 2 + 3y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 0.6y + y2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 0.6y + -0.4 + y2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 0.6y + y2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 0.6y + y2 = 0 + -0.4 0.6y + y2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 0.6y + y2 = -0.4 The y term is 0.6y. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6y + 0.09 + y2 = -0.4 + 0.09 Reorder the terms: 0.09 + 0.6y + y2 = -0.4 + 0.09 Combine like terms: -0.4 + 0.09 = -0.31 0.09 + 0.6y + y2 = -0.31 Factor a perfect square on the left side: (y + 0.3)(y + 0.3) = -0.31 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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