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Simplifying 5a * a + -26a + 15 = 0 Multiply a * a 5a2 + -26a + 15 = 0 Reorder the terms: 15 + -26a + 5a2 = 0 Solving 15 + -26a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + -5.2a + a2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5.2a + -3 + a2 = 0 + -3 Reorder the terms: 3 + -3 + -5.2a + a2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5.2a + a2 = 0 + -3 -5.2a + a2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5.2a + a2 = -3 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 = -3 + 6.76 Reorder the terms: 6.76 + -5.2a + a2 = -3 + 6.76 Combine like terms: -3 + 6.76 = 3.76 6.76 + -5.2a + a2 = 3.76 Factor a perfect square on the left side: (a + -2.6)(a + -2.6) = 3.76 Calculate the square root of the right side: 1.939071943 Break this problem into two subproblems by setting (a + -2.6) equal to 1.939071943 and -1.939071943.Subproblem 1
a + -2.6 = 1.939071943 Simplifying a + -2.6 = 1.939071943 Reorder the terms: -2.6 + a = 1.939071943 Solving -2.6 + a = 1.939071943 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 = 1.939071943 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + a = 1.939071943 + 2.6 a = 1.939071943 + 2.6 Combine like terms: 1.939071943 + 2.6 = 4.539071943 a = 4.539071943 Simplifying a = 4.539071943Subproblem 2
a + -2.6 = -1.939071943 Simplifying a + -2.6 = -1.939071943 Reorder the terms: -2.6 + a = -1.939071943 Solving -2.6 + a = -1.939071943 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 = -1.939071943 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + a = -1.939071943 + 2.6 a = -1.939071943 + 2.6 Combine like terms: -1.939071943 + 2.6 = 0.660928057 a = 0.660928057 Simplifying a = 0.660928057Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.539071943, 0.660928057}
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