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Simplifying 34 + -1(5 + 6y + -2)(y + 4) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) Reorder the terms: 34 + -1(5 + -2 + 6y)(y + 4) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) Combine like terms: 5 + -2 = 3 34 + -1(3 + 6y)(y + 4) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) Reorder the terms: 34 + -1(3 + 6y)(4 + y) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) Multiply (3 + 6y) * (4 + y) 34 + -1(3(4 + y) + 6y * (4 + y)) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) 34 + -1((4 * 3 + y * 3) + 6y * (4 + y)) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) 34 + -1((12 + 3y) + 6y * (4 + y)) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) 34 + -1(12 + 3y + (4 * 6y + y * 6y)) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) 34 + -1(12 + 3y + (24y + 6y2)) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) Combine like terms: 3y + 24y = 27y 34 + -1(12 + 27y + 6y2) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) 34 + (12 * -1 + 27y * -1 + 6y2 * -1) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) 34 + (-12 + -27y + -6y2) = -3(5y + -5) + -1(8(y + -1) + -13y + 10) Combine like terms: 34 + -12 = 22 22 + -27y + -6y2 = -3(5y + -5) + -1(8(y + -1) + -13y + 10) Reorder the terms: 22 + -27y + -6y2 = -3(-5 + 5y) + -1(8(y + -1) + -13y + 10) 22 + -27y + -6y2 = (-5 * -3 + 5y * -3) + -1(8(y + -1) + -13y + 10) 22 + -27y + -6y2 = (15 + -15y) + -1(8(y + -1) + -13y + 10) Reorder the terms: 22 + -27y + -6y2 = 15 + -15y + -1(8(-1 + y) + -13y + 10) 22 + -27y + -6y2 = 15 + -15y + -1((-1 * 8 + y * 8) + -13y + 10) 22 + -27y + -6y2 = 15 + -15y + -1((-8 + 8y) + -13y + 10) Reorder the terms: 22 + -27y + -6y2 = 15 + -15y + -1(-8 + 10 + 8y + -13y) Combine like terms: -8 + 10 = 2 22 + -27y + -6y2 = 15 + -15y + -1(2 + 8y + -13y) Combine like terms: 8y + -13y = -5y 22 + -27y + -6y2 = 15 + -15y + -1(2 + -5y) 22 + -27y + -6y2 = 15 + -15y + (2 * -1 + -5y * -1) 22 + -27y + -6y2 = 15 + -15y + (-2 + 5y) Reorder the terms: 22 + -27y + -6y2 = 15 + -2 + -15y + 5y Combine like terms: 15 + -2 = 13 22 + -27y + -6y2 = 13 + -15y + 5y Combine like terms: -15y + 5y = -10y 22 + -27y + -6y2 = 13 + -10y Solving 22 + -27y + -6y2 = 13 + -10y Solving for variable 'y'. Reorder the terms: 22 + -13 + -27y + 10y + -6y2 = 13 + -10y + -13 + 10y Combine like terms: 22 + -13 = 9 9 + -27y + 10y + -6y2 = 13 + -10y + -13 + 10y Combine like terms: -27y + 10y = -17y 9 + -17y + -6y2 = 13 + -10y + -13 + 10y Reorder the terms: 9 + -17y + -6y2 = 13 + -13 + -10y + 10y Combine like terms: 13 + -13 = 0 9 + -17y + -6y2 = 0 + -10y + 10y 9 + -17y + -6y2 = -10y + 10y Combine like terms: -10y + 10y = 0 9 + -17y + -6y2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.5 + 2.833333333y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 2.833333333y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 2.833333333y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 2.833333333y + y2 = 0 + 1.5 2.833333333y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 2.833333333y + y2 = 1.5 The y term is 2.833333333y. Take half its coefficient (1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. 2.833333333y + 2.006944445 + y2 = 1.5 + 2.006944445 Reorder the terms: 2.006944445 + 2.833333333y + y2 = 1.5 + 2.006944445 Combine like terms: 1.5 + 2.006944445 = 3.506944445 2.006944445 + 2.833333333y + y2 = 3.506944445 Factor a perfect square on the left side: (y + 1.416666667)(y + 1.416666667) = 3.506944445 Calculate the square root of the right side: 1.872683755 Break this problem into two subproblems by setting (y + 1.416666667) equal to 1.872683755 and -1.872683755.Subproblem 1
y + 1.416666667 = 1.872683755 Simplifying y + 1.416666667 = 1.872683755 Reorder the terms: 1.416666667 + y = 1.872683755 Solving 1.416666667 + y = 1.872683755 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + y = 1.872683755 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + y = 1.872683755 + -1.416666667 y = 1.872683755 + -1.416666667 Combine like terms: 1.872683755 + -1.416666667 = 0.456017088 y = 0.456017088 Simplifying y = 0.456017088Subproblem 2
y + 1.416666667 = -1.872683755 Simplifying y + 1.416666667 = -1.872683755 Reorder the terms: 1.416666667 + y = -1.872683755 Solving 1.416666667 + y = -1.872683755 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + y = -1.872683755 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + y = -1.872683755 + -1.416666667 y = -1.872683755 + -1.416666667 Combine like terms: -1.872683755 + -1.416666667 = -3.289350422 y = -3.289350422 Simplifying y = -3.289350422Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.456017088, -3.289350422}
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