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Simplifying (5y2 + -6y + -54) = 0 Reorder the terms: (-54 + -6y + 5y2) = 0 Remove parenthesis around (-54 + -6y + 5y2) -54 + -6y + 5y2 = 0 Solving -54 + -6y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.8 + -1.2y + y2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + -1.2y + 10.8 + y2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + -1.2y + y2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + -1.2y + y2 = 0 + 10.8 -1.2y + y2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 -1.2y + y2 = 10.8 The y term is -1.2y. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2y + 0.36 + y2 = 10.8 + 0.36 Reorder the terms: 0.36 + -1.2y + y2 = 10.8 + 0.36 Combine like terms: 10.8 + 0.36 = 11.16 0.36 + -1.2y + y2 = 11.16 Factor a perfect square on the left side: (y + -0.6)(y + -0.6) = 11.16 Calculate the square root of the right side: 3.340658618 Break this problem into two subproblems by setting (y + -0.6) equal to 3.340658618 and -3.340658618.Subproblem 1
y + -0.6 = 3.340658618 Simplifying y + -0.6 = 3.340658618 Reorder the terms: -0.6 + y = 3.340658618 Solving -0.6 + y = 3.340658618 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = 3.340658618 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = 3.340658618 + 0.6 y = 3.340658618 + 0.6 Combine like terms: 3.340658618 + 0.6 = 3.940658618 y = 3.940658618 Simplifying y = 3.940658618Subproblem 2
y + -0.6 = -3.340658618 Simplifying y + -0.6 = -3.340658618 Reorder the terms: -0.6 + y = -3.340658618 Solving -0.6 + y = -3.340658618 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = -3.340658618 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = -3.340658618 + 0.6 y = -3.340658618 + 0.6 Combine like terms: -3.340658618 + 0.6 = -2.740658618 y = -2.740658618 Simplifying y = -2.740658618Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.940658618, -2.740658618}
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