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Simplifying 3a2 = 4a + 3 Reorder the terms: 3a2 = 3 + 4a Solving 3a2 = 3 + 4a Solving for variable 'a'. Reorder the terms: -3 + -4a + 3a2 = 3 + 4a + -3 + -4a Reorder the terms: -3 + -4a + 3a2 = 3 + -3 + 4a + -4a Combine like terms: 3 + -3 = 0 -3 + -4a + 3a2 = 0 + 4a + -4a -3 + -4a + 3a2 = 4a + -4a Combine like terms: 4a + -4a = 0 -3 + -4a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -1.333333333a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.333333333a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + -1.333333333a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.333333333a + a2 = 0 + 1 -1.333333333a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.333333333a + a2 = 1 The a term is -1.333333333a. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333a + 0.4444444442 + a2 = 1 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333a + a2 = 1 + 0.4444444442 Combine like terms: 1 + 0.4444444442 = 1.4444444442 0.4444444442 + -1.333333333a + a2 = 1.4444444442 Factor a perfect square on the left side: (a + -0.6666666665)(a + -0.6666666665) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (a + -0.6666666665) equal to 1.201850425 and -1.201850425.Subproblem 1
a + -0.6666666665 = 1.201850425 Simplifying a + -0.6666666665 = 1.201850425 Reorder the terms: -0.6666666665 + a = 1.201850425 Solving -0.6666666665 + a = 1.201850425 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + a = 1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + a = 1.201850425 + 0.6666666665 a = 1.201850425 + 0.6666666665 Combine like terms: 1.201850425 + 0.6666666665 = 1.8685170915 a = 1.8685170915 Simplifying a = 1.8685170915Subproblem 2
a + -0.6666666665 = -1.201850425 Simplifying a + -0.6666666665 = -1.201850425 Reorder the terms: -0.6666666665 + a = -1.201850425 Solving -0.6666666665 + a = -1.201850425 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + a = -1.201850425 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + a = -1.201850425 + 0.6666666665 a = -1.201850425 + 0.6666666665 Combine like terms: -1.201850425 + 0.6666666665 = -0.5351837585 a = -0.5351837585 Simplifying a = -0.5351837585Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.8685170915, -0.5351837585}
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