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Simplifying 4a2 + -2a = 24 Reorder the terms: -2a + 4a2 = 24 Solving -2a + 4a2 = 24 Solving for variable 'a'. Reorder the terms: -24 + -2a + 4a2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -2a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -1a + 2a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -1a + 2a2)' equal to zero and attempt to solve: Simplifying -12 + -1a + 2a2 = 0 Solving -12 + -1a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -0.5a + a2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.5a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + -0.5a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.5a + a2 = 0 + 6 -0.5a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.5a + a2 = 6 The a term is -0.5a. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a + 0.0625 + a2 = 6 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = 6 + 0.0625 Combine like terms: 6 + 0.0625 = 6.0625 0.0625 + -0.5a + a2 = 6.0625 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (a + -0.25) equal to 2.46221445 and -2.46221445.Subproblem 1
a + -0.25 = 2.46221445 Simplifying a + -0.25 = 2.46221445 Reorder the terms: -0.25 + a = 2.46221445 Solving -0.25 + a = 2.46221445 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 2.46221445 + 0.25 a = 2.46221445 + 0.25 Combine like terms: 2.46221445 + 0.25 = 2.71221445 a = 2.71221445 Simplifying a = 2.71221445Subproblem 2
a + -0.25 = -2.46221445 Simplifying a + -0.25 = -2.46221445 Reorder the terms: -0.25 + a = -2.46221445 Solving -0.25 + a = -2.46221445 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -2.46221445 + 0.25 a = -2.46221445 + 0.25 Combine like terms: -2.46221445 + 0.25 = -2.21221445 a = -2.21221445 Simplifying a = -2.21221445Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.71221445, -2.21221445}Solution
a = {2.71221445, -2.21221445}
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