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Simplifying 4a + -4(14 + -1a) * a = 7 Reorder the terms for easier multiplication: 4a + -4a(14 + -1a) = 7 4a + (14 * -4a + -1a * -4a) = 7 4a + (-56a + 4a2) = 7 Combine like terms: 4a + -56a = -52a -52a + 4a2 = 7 Solving -52a + 4a2 = 7 Solving for variable 'a'. Reorder the terms: -7 + -52a + 4a2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -52a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -13a + a2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -13a + 1.75 + a2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -13a + a2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -13a + a2 = 0 + 1.75 -13a + a2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -13a + a2 = 1.75 The a term is -13a. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13a + 42.25 + a2 = 1.75 + 42.25 Reorder the terms: 42.25 + -13a + a2 = 1.75 + 42.25 Combine like terms: 1.75 + 42.25 = 44 42.25 + -13a + a2 = 44 Factor a perfect square on the left side: (a + -6.5)(a + -6.5) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (a + -6.5) equal to 6.633249581 and -6.633249581.Subproblem 1
a + -6.5 = 6.633249581 Simplifying a + -6.5 = 6.633249581 Reorder the terms: -6.5 + a = 6.633249581 Solving -6.5 + a = 6.633249581 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + a = 6.633249581 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + a = 6.633249581 + 6.5 a = 6.633249581 + 6.5 Combine like terms: 6.633249581 + 6.5 = 13.133249581 a = 13.133249581 Simplifying a = 13.133249581Subproblem 2
a + -6.5 = -6.633249581 Simplifying a + -6.5 = -6.633249581 Reorder the terms: -6.5 + a = -6.633249581 Solving -6.5 + a = -6.633249581 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + a = -6.633249581 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + a = -6.633249581 + 6.5 a = -6.633249581 + 6.5 Combine like terms: -6.633249581 + 6.5 = -0.133249581 a = -0.133249581 Simplifying a = -0.133249581Solution
The solution to the problem is based on the solutions from the subproblems. a = {13.133249581, -0.133249581}
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