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Simplifying 18y + -21 = 3y2 + -24 Reorder the terms: -21 + 18y = 3y2 + -24 Reorder the terms: -21 + 18y = -24 + 3y2 Solving -21 + 18y = -24 + 3y2 Solving for variable 'y'. Reorder the terms: -21 + 24 + 18y + -3y2 = -24 + 3y2 + 24 + -3y2 Combine like terms: -21 + 24 = 3 3 + 18y + -3y2 = -24 + 3y2 + 24 + -3y2 Reorder the terms: 3 + 18y + -3y2 = -24 + 24 + 3y2 + -3y2 Combine like terms: -24 + 24 = 0 3 + 18y + -3y2 = 0 + 3y2 + -3y2 3 + 18y + -3y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 3 + 18y + -3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 6y + -1y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 6y + -1y2)' equal to zero and attempt to solve: Simplifying 1 + 6y + -1y2 = 0 Solving 1 + 6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -6y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -6y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6y + y2 = 0 + 1 -6y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6y + y2 = 1 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 1 + 9 Reorder the terms: 9 + -6y + y2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6y + y2 = 10 Factor a perfect square on the left side: (y + -3)(y + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
y + -3 = 3.16227766 Simplifying y + -3 = 3.16227766 Reorder the terms: -3 + y = 3.16227766 Solving -3 + y = 3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + y = 3.16227766 + 3 y = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 y = 6.16227766 Simplifying y = 6.16227766Subproblem 2
y + -3 = -3.16227766 Simplifying y + -3 = -3.16227766 Reorder the terms: -3 + y = -3.16227766 Solving -3 + y = -3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + y = -3.16227766 + 3 y = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 y = -0.16227766 Simplifying y = -0.16227766Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.16227766, -0.16227766}Solution
y = {6.16227766, -0.16227766}
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