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Simplifying 28 + -6y = 12y2 Solving 28 + -6y = 12y2 Solving for variable 'y'. Combine like terms: 12y2 + -12y2 = 0 28 + -6y + -12y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -3y + -6y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + -3y + -6y2)' equal to zero and attempt to solve: Simplifying 14 + -3y + -6y2 = 0 Solving 14 + -3y + -6y2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2.333333333 + 0.5y + y2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 0.5y + 2.333333333 + y2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 0.5y + y2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 0.5y + y2 = 0 + 2.333333333 0.5y + y2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 0.5y + y2 = 2.333333333 The y term is 0.5y. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5y + 0.0625 + y2 = 2.333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5y + y2 = 2.333333333 + 0.0625 Combine like terms: 2.333333333 + 0.0625 = 2.395833333 0.0625 + 0.5y + y2 = 2.395833333 Factor a perfect square on the left side: (y + 0.25)(y + 0.25) = 2.395833333 Calculate the square root of the right side: 1.547847968 Break this problem into two subproblems by setting (y + 0.25) equal to 1.547847968 and -1.547847968.Subproblem 1
y + 0.25 = 1.547847968 Simplifying y + 0.25 = 1.547847968 Reorder the terms: 0.25 + y = 1.547847968 Solving 0.25 + y = 1.547847968 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y = 1.547847968 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y = 1.547847968 + -0.25 y = 1.547847968 + -0.25 Combine like terms: 1.547847968 + -0.25 = 1.297847968 y = 1.297847968 Simplifying y = 1.297847968Subproblem 2
y + 0.25 = -1.547847968 Simplifying y + 0.25 = -1.547847968 Reorder the terms: 0.25 + y = -1.547847968 Solving 0.25 + y = -1.547847968 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y = -1.547847968 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y = -1.547847968 + -0.25 y = -1.547847968 + -0.25 Combine like terms: -1.547847968 + -0.25 = -1.797847968 y = -1.797847968 Simplifying y = -1.797847968Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.297847968, -1.797847968}Solution
y = {1.297847968, -1.797847968}
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