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Simplifying 5a2 + -4a + -4 = 3 Reorder the terms: -4 + -4a + 5a2 = 3 Solving -4 + -4a + 5a2 = 3 Solving for variable 'a'. Reorder the terms: -4 + -3 + -4a + 5a2 = 3 + -3 Combine like terms: -4 + -3 = -7 -7 + -4a + 5a2 = 3 + -3 Combine like terms: 3 + -3 = 0 -7 + -4a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.8a + a2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.8a + 1.4 + a2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.8a + a2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.8a + a2 = 0 + 1.4 -0.8a + a2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.8a + a2 = 1.4 The a term is -0.8a. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8a + 0.16 + a2 = 1.4 + 0.16 Reorder the terms: 0.16 + -0.8a + a2 = 1.4 + 0.16 Combine like terms: 1.4 + 0.16 = 1.56 0.16 + -0.8a + a2 = 1.56 Factor a perfect square on the left side: (a + -0.4)(a + -0.4) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (a + -0.4) equal to 1.2489996 and -1.2489996.Subproblem 1
a + -0.4 = 1.2489996 Simplifying a + -0.4 = 1.2489996 Reorder the terms: -0.4 + a = 1.2489996 Solving -0.4 + a = 1.2489996 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + a = 1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + a = 1.2489996 + 0.4 a = 1.2489996 + 0.4 Combine like terms: 1.2489996 + 0.4 = 1.6489996 a = 1.6489996 Simplifying a = 1.6489996Subproblem 2
a + -0.4 = -1.2489996 Simplifying a + -0.4 = -1.2489996 Reorder the terms: -0.4 + a = -1.2489996 Solving -0.4 + a = -1.2489996 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + a = -1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + a = -1.2489996 + 0.4 a = -1.2489996 + 0.4 Combine like terms: -1.2489996 + 0.4 = -0.8489996 a = -0.8489996 Simplifying a = -0.8489996Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.6489996, -0.8489996}
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