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Simplifying (4y2 + -6y + 7) + -1(2y + -6 + 3) = 0 Reorder the terms: (7 + -6y + 4y2) + -1(2y + -6 + 3) = 0 Remove parenthesis around (7 + -6y + 4y2) 7 + -6y + 4y2 + -1(2y + -6 + 3) = 0 Reorder the terms: 7 + -6y + 4y2 + -1(-6 + 3 + 2y) = 0 Combine like terms: -6 + 3 = -3 7 + -6y + 4y2 + -1(-3 + 2y) = 0 7 + -6y + 4y2 + (-3 * -1 + 2y * -1) = 0 7 + -6y + 4y2 + (3 + -2y) = 0 Reorder the terms: 7 + 3 + -6y + -2y + 4y2 = 0 Combine like terms: 7 + 3 = 10 10 + -6y + -2y + 4y2 = 0 Combine like terms: -6y + -2y = -8y 10 + -8y + 4y2 = 0 Solving 10 + -8y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -4y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -4y + 2y2)' equal to zero and attempt to solve: Simplifying 5 + -4y + 2y2 = 0 Solving 5 + -4y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -2y + y2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -2y + -2.5 + y2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -2y + y2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -2y + y2 = 0 + -2.5 -2y + y2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -2y + y2 = -2.5 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = -2.5 + 1 Reorder the terms: 1 + -2y + y2 = -2.5 + 1 Combine like terms: -2.5 + 1 = -1.5 1 + -2y + y2 = -1.5 Factor a perfect square on the left side: (y + -1)(y + -1) = -1.5 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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