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Simplifying 6.4a2 = 1 + -7.2a Solving 6.4a2 = 1 + -7.2a Solving for variable 'a'. Reorder the terms: -1 + 7.2a + 6.4a2 = 1 + -7.2a + -1 + 7.2a Reorder the terms: -1 + 7.2a + 6.4a2 = 1 + -1 + -7.2a + 7.2a Combine like terms: 1 + -1 = 0 -1 + 7.2a + 6.4a2 = 0 + -7.2a + 7.2a -1 + 7.2a + 6.4a2 = -7.2a + 7.2a Combine like terms: -7.2a + 7.2a = 0.0 -1 + 7.2a + 6.4a2 = 0.0 Begin completing the square. Divide all terms by 6.4 the coefficient of the squared term: Divide each side by '6.4'. -0.15625 + 1.125a + a2 = 0 Move the constant term to the right: Add '0.15625' to each side of the equation. -0.15625 + 1.125a + 0.15625 + a2 = 0 + 0.15625 Reorder the terms: -0.15625 + 0.15625 + 1.125a + a2 = 0 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + 1.125a + a2 = 0 + 0.15625 1.125a + a2 = 0 + 0.15625 Combine like terms: 0 + 0.15625 = 0.15625 1.125a + a2 = 0.15625 The a term is 1.125a. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125a + 0.31640625 + a2 = 0.15625 + 0.31640625 Reorder the terms: 0.31640625 + 1.125a + a2 = 0.15625 + 0.31640625 Combine like terms: 0.15625 + 0.31640625 = 0.47265625 0.31640625 + 1.125a + a2 = 0.47265625 Factor a perfect square on the left side: (a + 0.5625)(a + 0.5625) = 0.47265625 Calculate the square root of the right side: 0.6875 Break this problem into two subproblems by setting (a + 0.5625) equal to 0.6875 and -0.6875.Subproblem 1
a + 0.5625 = 0.6875 Simplifying a + 0.5625 = 0.6875 Reorder the terms: 0.5625 + a = 0.6875 Solving 0.5625 + a = 0.6875 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + a = 0.6875 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + a = 0.6875 + -0.5625 a = 0.6875 + -0.5625 Combine like terms: 0.6875 + -0.5625 = 0.125 a = 0.125 Simplifying a = 0.125Subproblem 2
a + 0.5625 = -0.6875 Simplifying a + 0.5625 = -0.6875 Reorder the terms: 0.5625 + a = -0.6875 Solving 0.5625 + a = -0.6875 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + a = -0.6875 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + a = -0.6875 + -0.5625 a = -0.6875 + -0.5625 Combine like terms: -0.6875 + -0.5625 = -1.25 a = -1.25 Simplifying a = -1.25Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.125, -1.25}
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