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Simplifying (4y + 11) = (3y2 + -2y + -7) Reorder the terms: (11 + 4y) = (3y2 + -2y + -7) Remove parenthesis around (11 + 4y) 11 + 4y = (3y2 + -2y + -7) Reorder the terms: 11 + 4y = (-7 + -2y + 3y2) Remove parenthesis around (-7 + -2y + 3y2) 11 + 4y = -7 + -2y + 3y2 Solving 11 + 4y = -7 + -2y + 3y2 Solving for variable 'y'. Reorder the terms: 11 + 7 + 4y + 2y + -3y2 = -7 + -2y + 3y2 + 7 + 2y + -3y2 Combine like terms: 11 + 7 = 18 18 + 4y + 2y + -3y2 = -7 + -2y + 3y2 + 7 + 2y + -3y2 Combine like terms: 4y + 2y = 6y 18 + 6y + -3y2 = -7 + -2y + 3y2 + 7 + 2y + -3y2 Reorder the terms: 18 + 6y + -3y2 = -7 + 7 + -2y + 2y + 3y2 + -3y2 Combine like terms: -7 + 7 = 0 18 + 6y + -3y2 = 0 + -2y + 2y + 3y2 + -3y2 18 + 6y + -3y2 = -2y + 2y + 3y2 + -3y2 Combine like terms: -2y + 2y = 0 18 + 6y + -3y2 = 0 + 3y2 + -3y2 18 + 6y + -3y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 18 + 6y + -3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + 2y + -1y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + 2y + -1y2)' equal to zero and attempt to solve: Simplifying 6 + 2y + -1y2 = 0 Solving 6 + 2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + -2y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -2y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2y + y2 = 0 + 6 -2y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2y + y2 = 6 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 = 6 + 1 Reorder the terms: 1 + -2y + y2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2y + y2 = 7 Factor a perfect square on the left side: (y + -1)(y + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
y + -1 = 2.645751311 Simplifying y + -1 = 2.645751311 Reorder the terms: -1 + y = 2.645751311 Solving -1 + y = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + y = 2.645751311 + 1 y = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 y = 3.645751311 Simplifying y = 3.645751311Subproblem 2
y + -1 = -2.645751311 Simplifying y + -1 = -2.645751311 Reorder the terms: -1 + y = -2.645751311 Solving -1 + y = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + y = -2.645751311 + 1 y = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 y = -1.645751311 Simplifying y = -1.645751311Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.645751311, -1.645751311}Solution
y = {3.645751311, -1.645751311}
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