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Simplifying 5a2 + -26a + -12 = 0 Reorder the terms: -12 + -26a + 5a2 = 0 Solving -12 + -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'. -2.4 + -5.2a + a2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -5.2a + 2.4 + a2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -5.2a + a2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -5.2a + a2 = 0 + 2.4 -5.2a + a2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -5.2a + a2 = 2.4 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 = 2.4 + 6.76 Reorder the terms: 6.76 + -5.2a + a2 = 2.4 + 6.76 Combine like terms: 2.4 + 6.76 = 9.16 6.76 + -5.2a + a2 = 9.16 Factor a perfect square on the left side: (a + -2.6)(a + -2.6) = 9.16 Calculate the square root of the right side: 3.02654919 Break this problem into two subproblems by setting (a + -2.6) equal to 3.02654919 and -3.02654919.Subproblem 1
a + -2.6 = 3.02654919 Simplifying a + -2.6 = 3.02654919 Reorder the terms: -2.6 + a = 3.02654919 Solving -2.6 + a = 3.02654919 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 = 3.02654919 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + a = 3.02654919 + 2.6 a = 3.02654919 + 2.6 Combine like terms: 3.02654919 + 2.6 = 5.62654919 a = 5.62654919 Simplifying a = 5.62654919Subproblem 2
a + -2.6 = -3.02654919 Simplifying a + -2.6 = -3.02654919 Reorder the terms: -2.6 + a = -3.02654919 Solving -2.6 + a = -3.02654919 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 = -3.02654919 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + a = -3.02654919 + 2.6 a = -3.02654919 + 2.6 Combine like terms: -3.02654919 + 2.6 = -0.42654919 a = -0.42654919 Simplifying a = -0.42654919Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.62654919, -0.42654919}
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