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Simplifying (5y2 + -7y + 3) + (-2y2 + 4y + 1) = 0 Reorder the terms: (3 + -7y + 5y2) + (-2y2 + 4y + 1) = 0 Remove parenthesis around (3 + -7y + 5y2) 3 + -7y + 5y2 + (-2y2 + 4y + 1) = 0 Reorder the terms: 3 + -7y + 5y2 + (1 + 4y + -2y2) = 0 Remove parenthesis around (1 + 4y + -2y2) 3 + -7y + 5y2 + 1 + 4y + -2y2 = 0 Reorder the terms: 3 + 1 + -7y + 4y + 5y2 + -2y2 = 0 Combine like terms: 3 + 1 = 4 4 + -7y + 4y + 5y2 + -2y2 = 0 Combine like terms: -7y + 4y = -3y 4 + -3y + 5y2 + -2y2 = 0 Combine like terms: 5y2 + -2y2 = 3y2 4 + -3y + 3y2 = 0 Solving 4 + -3y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -1y + y2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -1y + -1.333333333 + y2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -1y + y2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -1y + y2 = 0 + -1.333333333 -1y + y2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -1y + y2 = -1.333333333 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = -1.333333333 + 0.25 Reorder the terms: 0.25 + -1y + y2 = -1.333333333 + 0.25 Combine like terms: -1.333333333 + 0.25 = -1.083333333 0.25 + -1y + y2 = -1.083333333 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = -1.083333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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