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Simplifying 6y = 8y2 + -8 Reorder the terms: 6y = -8 + 8y2 Solving 6y = -8 + 8y2 Solving for variable 'y'. Reorder the terms: 8 + 6y + -8y2 = -8 + 8y2 + 8 + -8y2 Reorder the terms: 8 + 6y + -8y2 = -8 + 8 + 8y2 + -8y2 Combine like terms: -8 + 8 = 0 8 + 6y + -8y2 = 0 + 8y2 + -8y2 8 + 6y + -8y2 = 8y2 + -8y2 Combine like terms: 8y2 + -8y2 = 0 8 + 6y + -8y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 3y + -4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 3y + -4y2)' equal to zero and attempt to solve: Simplifying 4 + 3y + -4y2 = 0 Solving 4 + 3y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1 + -0.75y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.75y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -0.75y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.75y + y2 = 0 + 1 -0.75y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.75y + y2 = 1 The y term is -0.75y. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75y + 0.140625 + y2 = 1 + 0.140625 Reorder the terms: 0.140625 + -0.75y + y2 = 1 + 0.140625 Combine like terms: 1 + 0.140625 = 1.140625 0.140625 + -0.75y + y2 = 1.140625 Factor a perfect square on the left side: (y + -0.375)(y + -0.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (y + -0.375) equal to 1.068000468 and -1.068000468.Subproblem 1
y + -0.375 = 1.068000468 Simplifying y + -0.375 = 1.068000468 Reorder the terms: -0.375 + y = 1.068000468 Solving -0.375 + y = 1.068000468 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = 1.068000468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = 1.068000468 + 0.375 y = 1.068000468 + 0.375 Combine like terms: 1.068000468 + 0.375 = 1.443000468 y = 1.443000468 Simplifying y = 1.443000468Subproblem 2
y + -0.375 = -1.068000468 Simplifying y + -0.375 = -1.068000468 Reorder the terms: -0.375 + y = -1.068000468 Solving -0.375 + y = -1.068000468 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = -1.068000468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = -1.068000468 + 0.375 y = -1.068000468 + 0.375 Combine like terms: -1.068000468 + 0.375 = -0.693000468 y = -0.693000468 Simplifying y = -0.693000468Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.443000468, -0.693000468}Solution
y = {1.443000468, -0.693000468}
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