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Simplifying (-5y2 + 3y + -21) + -1(-4y2 + -5y + 23) = 0 Reorder the terms: (-21 + 3y + -5y2) + -1(-4y2 + -5y + 23) = 0 Remove parenthesis around (-21 + 3y + -5y2) -21 + 3y + -5y2 + -1(-4y2 + -5y + 23) = 0 Reorder the terms: -21 + 3y + -5y2 + -1(23 + -5y + -4y2) = 0 -21 + 3y + -5y2 + (23 * -1 + -5y * -1 + -4y2 * -1) = 0 -21 + 3y + -5y2 + (-23 + 5y + 4y2) = 0 Reorder the terms: -21 + -23 + 3y + 5y + -5y2 + 4y2 = 0 Combine like terms: -21 + -23 = -44 -44 + 3y + 5y + -5y2 + 4y2 = 0 Combine like terms: 3y + 5y = 8y -44 + 8y + -5y2 + 4y2 = 0 Combine like terms: -5y2 + 4y2 = -1y2 -44 + 8y + -1y2 = 0 Solving -44 + 8y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 44 + -8y + y2 = 0 Move the constant term to the right: Add '-44' to each side of the equation. 44 + -8y + -44 + y2 = 0 + -44 Reorder the terms: 44 + -44 + -8y + y2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -8y + y2 = 0 + -44 -8y + y2 = 0 + -44 Combine like terms: 0 + -44 = -44 -8y + y2 = -44 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = -44 + 16 Reorder the terms: 16 + -8y + y2 = -44 + 16 Combine like terms: -44 + 16 = -28 16 + -8y + y2 = -28 Factor a perfect square on the left side: (y + -4)(y + -4) = -28 Can't calculate square root of the right side. The solution to this equation could not be determined.
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