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Simplifying 464 + -1a2 = a + -3 Reorder the terms: 464 + -1a2 = -3 + a Solving 464 + -1a2 = -3 + a Solving for variable 'a'. Reorder the terms: 464 + 3 + -1a + -1a2 = -3 + a + 3 + -1a Combine like terms: 464 + 3 = 467 467 + -1a + -1a2 = -3 + a + 3 + -1a Reorder the terms: 467 + -1a + -1a2 = -3 + 3 + a + -1a Combine like terms: -3 + 3 = 0 467 + -1a + -1a2 = 0 + a + -1a 467 + -1a + -1a2 = a + -1a Combine like terms: a + -1a = 0 467 + -1a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -467 + a + a2 = 0 Move the constant term to the right: Add '467' to each side of the equation. -467 + a + 467 + a2 = 0 + 467 Reorder the terms: -467 + 467 + a + a2 = 0 + 467 Combine like terms: -467 + 467 = 0 0 + a + a2 = 0 + 467 a + a2 = 0 + 467 Combine like terms: 0 + 467 = 467 a + a2 = 467 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = 467 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 467 + 0.25 Combine like terms: 467 + 0.25 = 467.25 1.25 + a2 = 467.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 467.25 Calculate the square root of the right side: 21.615966321 Break this problem into two subproblems by setting (a + 0.5) equal to 21.615966321 and -21.615966321.Subproblem 1
a + 0.5 = 21.615966321 Simplifying a + 0.5 = 21.615966321 Reorder the terms: 0.5 + a = 21.615966321 Solving 0.5 + a = 21.615966321 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 21.615966321 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 21.615966321 + -0.5 a = 21.615966321 + -0.5 Combine like terms: 21.615966321 + -0.5 = 21.115966321 a = 21.115966321 Simplifying a = 21.115966321Subproblem 2
a + 0.5 = -21.615966321 Simplifying a + 0.5 = -21.615966321 Reorder the terms: 0.5 + a = -21.615966321 Solving 0.5 + a = -21.615966321 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -21.615966321 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -21.615966321 + -0.5 a = -21.615966321 + -0.5 Combine like terms: -21.615966321 + -0.5 = -22.115966321 a = -22.115966321 Simplifying a = -22.115966321Solution
The solution to the problem is based on the solutions from the subproblems. a = {21.115966321, -22.115966321}
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