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Simplifying 2a2 + -14a + -12 = 0 Reorder the terms: -12 + -14a + 2a2 = 0 Solving -12 + -14a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -7a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -7a + a2)' equal to zero and attempt to solve: Simplifying -6 + -7a + a2 = 0 Solving -6 + -7a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -7a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + -7a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7a + a2 = 0 + 6 -7a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 -7a + a2 = 6 The a term is -7a. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7a + 12.25 + a2 = 6 + 12.25 Reorder the terms: 12.25 + -7a + a2 = 6 + 12.25 Combine like terms: 6 + 12.25 = 18.25 12.25 + -7a + a2 = 18.25 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (a + -3.5) equal to 4.272001873 and -4.272001873.Subproblem 1
a + -3.5 = 4.272001873 Simplifying a + -3.5 = 4.272001873 Reorder the terms: -3.5 + a = 4.272001873 Solving -3.5 + a = 4.272001873 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = 4.272001873 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 4.272001873 + 3.5 a = 4.272001873 + 3.5 Combine like terms: 4.272001873 + 3.5 = 7.772001873 a = 7.772001873 Simplifying a = 7.772001873Subproblem 2
a + -3.5 = -4.272001873 Simplifying a + -3.5 = -4.272001873 Reorder the terms: -3.5 + a = -4.272001873 Solving -3.5 + a = -4.272001873 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = -4.272001873 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -4.272001873 + 3.5 a = -4.272001873 + 3.5 Combine like terms: -4.272001873 + 3.5 = -0.772001873 a = -0.772001873 Simplifying a = -0.772001873Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.772001873, -0.772001873}Solution
a = {7.772001873, -0.772001873}
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