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Simplifying 2y2 + 4y + -18 = 0 Reorder the terms: -18 + 4y + 2y2 = 0 Solving -18 + 4y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 2y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 2y + y2)' equal to zero and attempt to solve: Simplifying -9 + 2y + y2 = 0 Solving -9 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 2y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + 2y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2y + y2 = 0 + 9 2y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 2y + y2 = 9 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 = 9 + 1 Reorder the terms: 1 + 2y + y2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + 2y + y2 = 10 Factor a perfect square on the left side: (y + 1)(y + 1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y + 1) equal to 3.16227766 and -3.16227766.Subproblem 1
y + 1 = 3.16227766 Simplifying y + 1 = 3.16227766 Reorder the terms: 1 + y = 3.16227766 Solving 1 + y = 3.16227766 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 = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + y = 3.16227766 + -1 y = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 y = 2.16227766 Simplifying y = 2.16227766Subproblem 2
y + 1 = -3.16227766 Simplifying y + 1 = -3.16227766 Reorder the terms: 1 + y = -3.16227766 Solving 1 + y = -3.16227766 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 = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + y = -3.16227766 + -1 y = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 y = -4.16227766 Simplifying y = -4.16227766Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.16227766, -4.16227766}Solution
y = {2.16227766, -4.16227766}
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