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Simplifying 4a3 + -4a2 + -49a = 0 Reorder the terms: -49a + -4a2 + 4a3 = 0 Solving -49a + -4a2 + 4a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-49 + -4a + 4a2) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-49 + -4a + 4a2)' equal to zero and attempt to solve: Simplifying -49 + -4a + 4a2 = 0 Solving -49 + -4a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + -1a + a2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + -1a + 12.25 + a2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + -1a + a2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + -1a + a2 = 0 + 12.25 -1a + a2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 -1a + a2 = 12.25 The a term is -1a. 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. -1a + 0.25 + a2 = 12.25 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 12.25 + 0.25 Combine like terms: 12.25 + 0.25 = 12.5 0.25 + -1a + a2 = 12.5 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (a + -0.5) equal to 3.535533906 and -3.535533906.Subproblem 1
a + -0.5 = 3.535533906 Simplifying a + -0.5 = 3.535533906 Reorder the terms: -0.5 + a = 3.535533906 Solving -0.5 + a = 3.535533906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 3.535533906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 3.535533906 + 0.5 a = 3.535533906 + 0.5 Combine like terms: 3.535533906 + 0.5 = 4.035533906 a = 4.035533906 Simplifying a = 4.035533906Subproblem 2
a + -0.5 = -3.535533906 Simplifying a + -0.5 = -3.535533906 Reorder the terms: -0.5 + a = -3.535533906 Solving -0.5 + a = -3.535533906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -3.535533906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -3.535533906 + 0.5 a = -3.535533906 + 0.5 Combine like terms: -3.535533906 + 0.5 = -3.035533906 a = -3.035533906 Simplifying a = -3.035533906Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.035533906, -3.035533906}Solution
a = {0, 4.035533906, -3.035533906}
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