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Simplifying 5a2 = 26a + 14 Reorder the terms: 5a2 = 14 + 26a Solving 5a2 = 14 + 26a Solving for variable 'a'. Reorder the terms: -14 + -26a + 5a2 = 14 + 26a + -14 + -26a Reorder the terms: -14 + -26a + 5a2 = 14 + -14 + 26a + -26a Combine like terms: 14 + -14 = 0 -14 + -26a + 5a2 = 0 + 26a + -26a -14 + -26a + 5a2 = 26a + -26a Combine like terms: 26a + -26a = 0 -14 + -26a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -5.2a + a2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -5.2a + 2.8 + a2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -5.2a + a2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -5.2a + a2 = 0 + 2.8 -5.2a + a2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -5.2a + a2 = 2.8 The a term is -5.2a. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2a + 6.76 + a2 = 2.8 + 6.76 Reorder the terms: 6.76 + -5.2a + a2 = 2.8 + 6.76 Combine like terms: 2.8 + 6.76 = 9.56 6.76 + -5.2a + a2 = 9.56 Factor a perfect square on the left side: (a + -2.6)(a + -2.6) = 9.56 Calculate the square root of the right side: 3.091924967 Break this problem into two subproblems by setting (a + -2.6) equal to 3.091924967 and -3.091924967.Subproblem 1
a + -2.6 = 3.091924967 Simplifying a + -2.6 = 3.091924967 Reorder the terms: -2.6 + a = 3.091924967 Solving -2.6 + a = 3.091924967 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + a = 3.091924967 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + a = 3.091924967 + 2.6 a = 3.091924967 + 2.6 Combine like terms: 3.091924967 + 2.6 = 5.691924967 a = 5.691924967 Simplifying a = 5.691924967Subproblem 2
a + -2.6 = -3.091924967 Simplifying a + -2.6 = -3.091924967 Reorder the terms: -2.6 + a = -3.091924967 Solving -2.6 + a = -3.091924967 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + a = -3.091924967 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + a = -3.091924967 + 2.6 a = -3.091924967 + 2.6 Combine like terms: -3.091924967 + 2.6 = -0.491924967 a = -0.491924967 Simplifying a = -0.491924967Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.691924967, -0.491924967}
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