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Simplifying 21y2 + -21y + -39 = 0 Reorder the terms: -39 + -21y + 21y2 = 0 Solving -39 + -21y + 21y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + -7y + 7y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + -7y + 7y2)' equal to zero and attempt to solve: Simplifying -13 + -7y + 7y2 = 0 Solving -13 + -7y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + -1y + y2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + -1y + 1.857142857 + y2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + -1y + y2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + -1y + y2 = 0 + 1.857142857 -1y + y2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 -1y + y2 = 1.857142857 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 1.857142857 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 1.857142857 + 0.25 Combine like terms: 1.857142857 + 0.25 = 2.107142857 0.25 + -1y + y2 = 2.107142857 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 2.107142857 Calculate the square root of the right side: 1.451600102 Break this problem into two subproblems by setting (y + -0.5) equal to 1.451600102 and -1.451600102.Subproblem 1
y + -0.5 = 1.451600102 Simplifying y + -0.5 = 1.451600102 Reorder the terms: -0.5 + y = 1.451600102 Solving -0.5 + y = 1.451600102 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 1.451600102 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.451600102 + 0.5 y = 1.451600102 + 0.5 Combine like terms: 1.451600102 + 0.5 = 1.951600102 y = 1.951600102 Simplifying y = 1.951600102Subproblem 2
y + -0.5 = -1.451600102 Simplifying y + -0.5 = -1.451600102 Reorder the terms: -0.5 + y = -1.451600102 Solving -0.5 + y = -1.451600102 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -1.451600102 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.451600102 + 0.5 y = -1.451600102 + 0.5 Combine like terms: -1.451600102 + 0.5 = -0.951600102 y = -0.951600102 Simplifying y = -0.951600102Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.951600102, -0.951600102}Solution
y = {1.951600102, -0.951600102}
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