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Simplifying 12y2 + -28y + 4 = 1 Reorder the terms: 4 + -28y + 12y2 = 1 Solving 4 + -28y + 12y2 = 1 Solving for variable 'y'. Reorder the terms: 4 + -1 + -28y + 12y2 = 1 + -1 Combine like terms: 4 + -1 = 3 3 + -28y + 12y2 = 1 + -1 Combine like terms: 1 + -1 = 0 3 + -28y + 12y2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.25 + -2.333333333y + y2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -2.333333333y + -0.25 + y2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -2.333333333y + y2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -2.333333333y + y2 = 0 + -0.25 -2.333333333y + y2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -2.333333333y + y2 = -0.25 The y term is -2.333333333y. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333y + 1.361111112 + y2 = -0.25 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333y + y2 = -0.25 + 1.361111112 Combine like terms: -0.25 + 1.361111112 = 1.111111112 1.361111112 + -2.333333333y + y2 = 1.111111112 Factor a perfect square on the left side: (y + -1.166666667)(y + -1.166666667) = 1.111111112 Calculate the square root of the right side: 1.054092554 Break this problem into two subproblems by setting (y + -1.166666667) equal to 1.054092554 and -1.054092554.Subproblem 1
y + -1.166666667 = 1.054092554 Simplifying y + -1.166666667 = 1.054092554 Reorder the terms: -1.166666667 + y = 1.054092554 Solving -1.166666667 + y = 1.054092554 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = 1.054092554 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = 1.054092554 + 1.166666667 y = 1.054092554 + 1.166666667 Combine like terms: 1.054092554 + 1.166666667 = 2.220759221 y = 2.220759221 Simplifying y = 2.220759221Subproblem 2
y + -1.166666667 = -1.054092554 Simplifying y + -1.166666667 = -1.054092554 Reorder the terms: -1.166666667 + y = -1.054092554 Solving -1.166666667 + y = -1.054092554 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = -1.054092554 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = -1.054092554 + 1.166666667 y = -1.054092554 + 1.166666667 Combine like terms: -1.054092554 + 1.166666667 = 0.112574113 y = 0.112574113 Simplifying y = 0.112574113Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.220759221, 0.112574113}
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