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Simplifying 13.6 = (4 + -1a)(10 + -1a) Multiply (4 + -1a) * (10 + -1a) 13.6 = (4(10 + -1a) + -1a * (10 + -1a)) 13.6 = ((10 * 4 + -1a * 4) + -1a * (10 + -1a)) 13.6 = ((40 + -4a) + -1a * (10 + -1a)) 13.6 = (40 + -4a + (10 * -1a + -1a * -1a)) 13.6 = (40 + -4a + (-10a + 1a2)) Combine like terms: -4a + -10a = -14a 13.6 = (40 + -14a + 1a2) Solving 13.6 = 40 + -14a + 1a2 Solving for variable 'a'. Combine like terms: 13.6 + -40 = -26.4 -26.4 + 14a + -1a2 = 40 + -14a + 1a2 + -40 + 14a + -1a2 Reorder the terms: -26.4 + 14a + -1a2 = 40 + -40 + -14a + 14a + 1a2 + -1a2 Combine like terms: 40 + -40 = 0 -26.4 + 14a + -1a2 = 0 + -14a + 14a + 1a2 + -1a2 -26.4 + 14a + -1a2 = -14a + 14a + 1a2 + -1a2 Combine like terms: -14a + 14a = 0 -26.4 + 14a + -1a2 = 0 + 1a2 + -1a2 -26.4 + 14a + -1a2 = 1a2 + -1a2 Combine like terms: 1a2 + -1a2 = 0 -26.4 + 14a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 26.4 + -14a + a2 = 0 Move the constant term to the right: Add '-26.4' to each side of the equation. 26.4 + -14a + -26.4 + a2 = 0 + -26.4 Reorder the terms: 26.4 + -26.4 + -14a + a2 = 0 + -26.4 Combine like terms: 26.4 + -26.4 = 0.0 0.0 + -14a + a2 = 0 + -26.4 -14a + a2 = 0 + -26.4 Combine like terms: 0 + -26.4 = -26.4 -14a + a2 = -26.4 The a term is -14a. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14a + 49 + a2 = -26.4 + 49 Reorder the terms: 49 + -14a + a2 = -26.4 + 49 Combine like terms: -26.4 + 49 = 22.6 49 + -14a + a2 = 22.6 Factor a perfect square on the left side: (a + -7)(a + -7) = 22.6 Calculate the square root of the right side: 4.75394573 Break this problem into two subproblems by setting (a + -7) equal to 4.75394573 and -4.75394573.Subproblem 1
a + -7 = 4.75394573 Simplifying a + -7 = 4.75394573 Reorder the terms: -7 + a = 4.75394573 Solving -7 + a = 4.75394573 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = 4.75394573 + 7 Combine like terms: -7 + 7 = 0 0 + a = 4.75394573 + 7 a = 4.75394573 + 7 Combine like terms: 4.75394573 + 7 = 11.75394573 a = 11.75394573 Simplifying a = 11.75394573Subproblem 2
a + -7 = -4.75394573 Simplifying a + -7 = -4.75394573 Reorder the terms: -7 + a = -4.75394573 Solving -7 + a = -4.75394573 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = -4.75394573 + 7 Combine like terms: -7 + 7 = 0 0 + a = -4.75394573 + 7 a = -4.75394573 + 7 Combine like terms: -4.75394573 + 7 = 2.24605427 a = 2.24605427 Simplifying a = 2.24605427Solution
The solution to the problem is based on the solutions from the subproblems. a = {11.75394573, 2.24605427}
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