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Simplifying 2y2 + -16y = 6 Reorder the terms: -16y + 2y2 = 6 Solving -16y + 2y2 = 6 Solving for variable 'y'. Reorder the terms: -6 + -16y + 2y2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -16y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -8y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -8y + y2)' equal to zero and attempt to solve: Simplifying -3 + -8y + y2 = 0 Solving -3 + -8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -8y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + -8y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8y + y2 = 0 + 3 -8y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 -8y + y2 = 3 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 3 + 16 Reorder the terms: 16 + -8y + y2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + -8y + y2 = 19 Factor a perfect square on the left side: (y + -4)(y + -4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (y + -4) equal to 4.358898944 and -4.358898944.Subproblem 1
y + -4 = 4.358898944 Simplifying y + -4 = 4.358898944 Reorder the terms: -4 + y = 4.358898944 Solving -4 + y = 4.358898944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + y = 4.358898944 + 4 y = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 y = 8.358898944 Simplifying y = 8.358898944Subproblem 2
y + -4 = -4.358898944 Simplifying y + -4 = -4.358898944 Reorder the terms: -4 + y = -4.358898944 Solving -4 + y = -4.358898944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + y = -4.358898944 + 4 y = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 y = -0.358898944 Simplifying y = -0.358898944Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.358898944, -0.358898944}Solution
y = {8.358898944, -0.358898944}
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