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Simplifying 18 + -82y + 42y2 = 0 Solving 18 + -82y + 42y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -41y + 21y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -41y + 21y2)' equal to zero and attempt to solve: Simplifying 9 + -41y + 21y2 = 0 Solving 9 + -41y + 21y2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.4285714286 + -1.952380952y + y2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -1.952380952y + -0.4285714286 + y2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -1.952380952y + y2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -1.952380952y + y2 = 0 + -0.4285714286 -1.952380952y + y2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -1.952380952y + y2 = -0.4285714286 The y term is -1.952380952y. Take half its coefficient (-0.976190476). Square it (0.9529478454) and add it to both sides. Add '0.9529478454' to each side of the equation. -1.952380952y + 0.9529478454 + y2 = -0.4285714286 + 0.9529478454 Reorder the terms: 0.9529478454 + -1.952380952y + y2 = -0.4285714286 + 0.9529478454 Combine like terms: -0.4285714286 + 0.9529478454 = 0.5243764168 0.9529478454 + -1.952380952y + y2 = 0.5243764168 Factor a perfect square on the left side: (y + -0.976190476)(y + -0.976190476) = 0.5243764168 Calculate the square root of the right side: 0.724138396 Break this problem into two subproblems by setting (y + -0.976190476) equal to 0.724138396 and -0.724138396.Subproblem 1
y + -0.976190476 = 0.724138396 Simplifying y + -0.976190476 = 0.724138396 Reorder the terms: -0.976190476 + y = 0.724138396 Solving -0.976190476 + y = 0.724138396 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.976190476' to each side of the equation. -0.976190476 + 0.976190476 + y = 0.724138396 + 0.976190476 Combine like terms: -0.976190476 + 0.976190476 = 0.000000000 0.000000000 + y = 0.724138396 + 0.976190476 y = 0.724138396 + 0.976190476 Combine like terms: 0.724138396 + 0.976190476 = 1.700328872 y = 1.700328872 Simplifying y = 1.700328872Subproblem 2
y + -0.976190476 = -0.724138396 Simplifying y + -0.976190476 = -0.724138396 Reorder the terms: -0.976190476 + y = -0.724138396 Solving -0.976190476 + y = -0.724138396 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.976190476' to each side of the equation. -0.976190476 + 0.976190476 + y = -0.724138396 + 0.976190476 Combine like terms: -0.976190476 + 0.976190476 = 0.000000000 0.000000000 + y = -0.724138396 + 0.976190476 y = -0.724138396 + 0.976190476 Combine like terms: -0.724138396 + 0.976190476 = 0.25205208 y = 0.25205208 Simplifying y = 0.25205208Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.700328872, 0.25205208}Solution
y = {1.700328872, 0.25205208}
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