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Simplifying 4a2 + -12a + -153 = 0 Reorder the terms: -153 + -12a + 4a2 = 0 Solving -153 + -12a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -38.25 + -3a + a2 = 0 Move the constant term to the right: Add '38.25' to each side of the equation. -38.25 + -3a + 38.25 + a2 = 0 + 38.25 Reorder the terms: -38.25 + 38.25 + -3a + a2 = 0 + 38.25 Combine like terms: -38.25 + 38.25 = 0.00 0.00 + -3a + a2 = 0 + 38.25 -3a + a2 = 0 + 38.25 Combine like terms: 0 + 38.25 = 38.25 -3a + a2 = 38.25 The a term is -3a. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3a + 2.25 + a2 = 38.25 + 2.25 Reorder the terms: 2.25 + -3a + a2 = 38.25 + 2.25 Combine like terms: 38.25 + 2.25 = 40.5 2.25 + -3a + a2 = 40.5 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (a + -1.5) equal to 6.363961031 and -6.363961031.Subproblem 1
a + -1.5 = 6.363961031 Simplifying a + -1.5 = 6.363961031 Reorder the terms: -1.5 + a = 6.363961031 Solving -1.5 + a = 6.363961031 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 6.363961031 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 6.363961031 + 1.5 a = 6.363961031 + 1.5 Combine like terms: 6.363961031 + 1.5 = 7.863961031 a = 7.863961031 Simplifying a = 7.863961031Subproblem 2
a + -1.5 = -6.363961031 Simplifying a + -1.5 = -6.363961031 Reorder the terms: -1.5 + a = -6.363961031 Solving -1.5 + a = -6.363961031 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -6.363961031 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -6.363961031 + 1.5 a = -6.363961031 + 1.5 Combine like terms: -6.363961031 + 1.5 = -4.863961031 a = -4.863961031 Simplifying a = -4.863961031Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.863961031, -4.863961031}
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