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Simplifying 8(7y2 + -5y + 6) + -3(5y2 + -9y + 7) = 0 Reorder the terms: 8(6 + -5y + 7y2) + -3(5y2 + -9y + 7) = 0 (6 * 8 + -5y * 8 + 7y2 * 8) + -3(5y2 + -9y + 7) = 0 (48 + -40y + 56y2) + -3(5y2 + -9y + 7) = 0 Reorder the terms: 48 + -40y + 56y2 + -3(7 + -9y + 5y2) = 0 48 + -40y + 56y2 + (7 * -3 + -9y * -3 + 5y2 * -3) = 0 48 + -40y + 56y2 + (-21 + 27y + -15y2) = 0 Reorder the terms: 48 + -21 + -40y + 27y + 56y2 + -15y2 = 0 Combine like terms: 48 + -21 = 27 27 + -40y + 27y + 56y2 + -15y2 = 0 Combine like terms: -40y + 27y = -13y 27 + -13y + 56y2 + -15y2 = 0 Combine like terms: 56y2 + -15y2 = 41y2 27 + -13y + 41y2 = 0 Solving 27 + -13y + 41y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 41 the coefficient of the squared term: Divide each side by '41'. 0.6585365854 + -0.3170731707y + y2 = 0 Move the constant term to the right: Add '-0.6585365854' to each side of the equation. 0.6585365854 + -0.3170731707y + -0.6585365854 + y2 = 0 + -0.6585365854 Reorder the terms: 0.6585365854 + -0.6585365854 + -0.3170731707y + y2 = 0 + -0.6585365854 Combine like terms: 0.6585365854 + -0.6585365854 = 0.0000000000 0.0000000000 + -0.3170731707y + y2 = 0 + -0.6585365854 -0.3170731707y + y2 = 0 + -0.6585365854 Combine like terms: 0 + -0.6585365854 = -0.6585365854 -0.3170731707y + y2 = -0.6585365854 The y term is -0.3170731707y. Take half its coefficient (-0.1585365854). Square it (0.02513384891) and add it to both sides. Add '0.02513384891' to each side of the equation. -0.3170731707y + 0.02513384891 + y2 = -0.6585365854 + 0.02513384891 Reorder the terms: 0.02513384891 + -0.3170731707y + y2 = -0.6585365854 + 0.02513384891 Combine like terms: -0.6585365854 + 0.02513384891 = -0.63340273649 0.02513384891 + -0.3170731707y + y2 = -0.63340273649 Factor a perfect square on the left side: (y + -0.1585365854)(y + -0.1585365854) = -0.63340273649 Can't calculate square root of the right side. The solution to this equation could not be determined.
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