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Simplifying -6 + 26Y + 8Y2 = 0 Solving -6 + 26Y + 8Y2 = 0 Solving for variable 'Y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 13Y + 4Y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 13Y + 4Y2)' equal to zero and attempt to solve: Simplifying -3 + 13Y + 4Y2 = 0 Solving -3 + 13Y + 4Y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 3.25Y + Y2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 3.25Y + 0.75 + Y2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 3.25Y + Y2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 3.25Y + Y2 = 0 + 0.75 3.25Y + Y2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 3.25Y + Y2 = 0.75 The Y term is 3.25Y. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25Y + 2.640625 + Y2 = 0.75 + 2.640625 Reorder the terms: 2.640625 + 3.25Y + Y2 = 0.75 + 2.640625 Combine like terms: 0.75 + 2.640625 = 3.390625 2.640625 + 3.25Y + Y2 = 3.390625 Factor a perfect square on the left side: (Y + 1.625)(Y + 1.625) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (Y + 1.625) equal to 1.841364983 and -1.841364983.Subproblem 1
Y + 1.625 = 1.841364983 Simplifying Y + 1.625 = 1.841364983 Reorder the terms: 1.625 + Y = 1.841364983 Solving 1.625 + Y = 1.841364983 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + Y = 1.841364983 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + Y = 1.841364983 + -1.625 Y = 1.841364983 + -1.625 Combine like terms: 1.841364983 + -1.625 = 0.216364983 Y = 0.216364983 Simplifying Y = 0.216364983Subproblem 2
Y + 1.625 = -1.841364983 Simplifying Y + 1.625 = -1.841364983 Reorder the terms: 1.625 + Y = -1.841364983 Solving 1.625 + Y = -1.841364983 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + Y = -1.841364983 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + Y = -1.841364983 + -1.625 Y = -1.841364983 + -1.625 Combine like terms: -1.841364983 + -1.625 = -3.466364983 Y = -3.466364983 Simplifying Y = -3.466364983Solution
The solution to the problem is based on the solutions from the subproblems. Y = {0.216364983, -3.466364983}Solution
Y = {0.216364983, -3.466364983}
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