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Simplifying 4a(a + -4) = 5 Reorder the terms: 4a(-4 + a) = 5 (-4 * 4a + a * 4a) = 5 (-16a + 4a2) = 5 Solving -16a + 4a2 = 5 Solving for variable 'a'. Reorder the terms: -5 + -16a + 4a2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -16a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -4a + a2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -4a + 1.25 + a2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -4a + a2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -4a + a2 = 0 + 1.25 -4a + a2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -4a + a2 = 1.25 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 1.25 + 4 Reorder the terms: 4 + -4a + a2 = 1.25 + 4 Combine like terms: 1.25 + 4 = 5.25 4 + -4a + a2 = 5.25 Factor a perfect square on the left side: (a + -2)(a + -2) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (a + -2) equal to 2.291287847 and -2.291287847.Subproblem 1
a + -2 = 2.291287847 Simplifying a + -2 = 2.291287847 Reorder the terms: -2 + a = 2.291287847 Solving -2 + a = 2.291287847 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 2.291287847 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.291287847 + 2 a = 2.291287847 + 2 Combine like terms: 2.291287847 + 2 = 4.291287847 a = 4.291287847 Simplifying a = 4.291287847Subproblem 2
a + -2 = -2.291287847 Simplifying a + -2 = -2.291287847 Reorder the terms: -2 + a = -2.291287847 Solving -2 + a = -2.291287847 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -2.291287847 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.291287847 + 2 a = -2.291287847 + 2 Combine like terms: -2.291287847 + 2 = -0.291287847 a = -0.291287847 Simplifying a = -0.291287847Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.291287847, -0.291287847}
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