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Simplifying 8(6y2 + -2y + 7) + -3(6y2 + -4y + 4) = 0 Reorder the terms: 8(7 + -2y + 6y2) + -3(6y2 + -4y + 4) = 0 (7 * 8 + -2y * 8 + 6y2 * 8) + -3(6y2 + -4y + 4) = 0 (56 + -16y + 48y2) + -3(6y2 + -4y + 4) = 0 Reorder the terms: 56 + -16y + 48y2 + -3(4 + -4y + 6y2) = 0 56 + -16y + 48y2 + (4 * -3 + -4y * -3 + 6y2 * -3) = 0 56 + -16y + 48y2 + (-12 + 12y + -18y2) = 0 Reorder the terms: 56 + -12 + -16y + 12y + 48y2 + -18y2 = 0 Combine like terms: 56 + -12 = 44 44 + -16y + 12y + 48y2 + -18y2 = 0 Combine like terms: -16y + 12y = -4y 44 + -4y + 48y2 + -18y2 = 0 Combine like terms: 48y2 + -18y2 = 30y2 44 + -4y + 30y2 = 0 Solving 44 + -4y + 30y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(22 + -2y + 15y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(22 + -2y + 15y2)' equal to zero and attempt to solve: Simplifying 22 + -2y + 15y2 = 0 Solving 22 + -2y + 15y2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.466666667 + -0.1333333333y + y2 = 0 Move the constant term to the right: Add '-1.466666667' to each side of the equation. 1.466666667 + -0.1333333333y + -1.466666667 + y2 = 0 + -1.466666667 Reorder the terms: 1.466666667 + -1.466666667 + -0.1333333333y + y2 = 0 + -1.466666667 Combine like terms: 1.466666667 + -1.466666667 = 0.000000000 0.000000000 + -0.1333333333y + y2 = 0 + -1.466666667 -0.1333333333y + y2 = 0 + -1.466666667 Combine like terms: 0 + -1.466666667 = -1.466666667 -0.1333333333y + y2 = -1.466666667 The y term is -0.1333333333y. Take half its coefficient (-0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. -0.1333333333y + 0.004444444442 + y2 = -1.466666667 + 0.004444444442 Reorder the terms: 0.004444444442 + -0.1333333333y + y2 = -1.466666667 + 0.004444444442 Combine like terms: -1.466666667 + 0.004444444442 = -1.462222222558 0.004444444442 + -0.1333333333y + y2 = -1.462222222558 Factor a perfect square on the left side: (y + -0.06666666665)(y + -0.06666666665) = -1.462222222558 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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