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Simplifying -5a2 + 8a = -162 Reorder the terms: 8a + -5a2 = -162 Solving 8a + -5a2 = -162 Solving for variable 'a'. Reorder the terms: 162 + 8a + -5a2 = -162 + 162 Combine like terms: -162 + 162 = 0 162 + 8a + -5a2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -32.4 + -1.6a + a2 = 0 Move the constant term to the right: Add '32.4' to each side of the equation. -32.4 + -1.6a + 32.4 + a2 = 0 + 32.4 Reorder the terms: -32.4 + 32.4 + -1.6a + a2 = 0 + 32.4 Combine like terms: -32.4 + 32.4 = 0.0 0.0 + -1.6a + a2 = 0 + 32.4 -1.6a + a2 = 0 + 32.4 Combine like terms: 0 + 32.4 = 32.4 -1.6a + a2 = 32.4 The a term is -1.6a. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6a + 0.64 + a2 = 32.4 + 0.64 Reorder the terms: 0.64 + -1.6a + a2 = 32.4 + 0.64 Combine like terms: 32.4 + 0.64 = 33.04 0.64 + -1.6a + a2 = 33.04 Factor a perfect square on the left side: (a + -0.8)(a + -0.8) = 33.04 Calculate the square root of the right side: 5.748043145 Break this problem into two subproblems by setting (a + -0.8) equal to 5.748043145 and -5.748043145.Subproblem 1
a + -0.8 = 5.748043145 Simplifying a + -0.8 = 5.748043145 Reorder the terms: -0.8 + a = 5.748043145 Solving -0.8 + a = 5.748043145 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + a = 5.748043145 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + a = 5.748043145 + 0.8 a = 5.748043145 + 0.8 Combine like terms: 5.748043145 + 0.8 = 6.548043145 a = 6.548043145 Simplifying a = 6.548043145Subproblem 2
a + -0.8 = -5.748043145 Simplifying a + -0.8 = -5.748043145 Reorder the terms: -0.8 + a = -5.748043145 Solving -0.8 + a = -5.748043145 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + a = -5.748043145 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + a = -5.748043145 + 0.8 a = -5.748043145 + 0.8 Combine like terms: -5.748043145 + 0.8 = -4.948043145 a = -4.948043145 Simplifying a = -4.948043145Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.548043145, -4.948043145}
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