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Simplifying 4a2 + -23a + 5 = 144 Reorder the terms: 5 + -23a + 4a2 = 144 Solving 5 + -23a + 4a2 = 144 Solving for variable 'a'. Reorder the terms: 5 + -144 + -23a + 4a2 = 144 + -144 Combine like terms: 5 + -144 = -139 -139 + -23a + 4a2 = 144 + -144 Combine like terms: 144 + -144 = 0 -139 + -23a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -34.75 + -5.75a + a2 = 0 Move the constant term to the right: Add '34.75' to each side of the equation. -34.75 + -5.75a + 34.75 + a2 = 0 + 34.75 Reorder the terms: -34.75 + 34.75 + -5.75a + a2 = 0 + 34.75 Combine like terms: -34.75 + 34.75 = 0.00 0.00 + -5.75a + a2 = 0 + 34.75 -5.75a + a2 = 0 + 34.75 Combine like terms: 0 + 34.75 = 34.75 -5.75a + a2 = 34.75 The a term is -5.75a. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75a + 8.265625 + a2 = 34.75 + 8.265625 Reorder the terms: 8.265625 + -5.75a + a2 = 34.75 + 8.265625 Combine like terms: 34.75 + 8.265625 = 43.015625 8.265625 + -5.75a + a2 = 43.015625 Factor a perfect square on the left side: (a + -2.875)(a + -2.875) = 43.015625 Calculate the square root of the right side: 6.558629811 Break this problem into two subproblems by setting (a + -2.875) equal to 6.558629811 and -6.558629811.Subproblem 1
a + -2.875 = 6.558629811 Simplifying a + -2.875 = 6.558629811 Reorder the terms: -2.875 + a = 6.558629811 Solving -2.875 + a = 6.558629811 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + a = 6.558629811 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + a = 6.558629811 + 2.875 a = 6.558629811 + 2.875 Combine like terms: 6.558629811 + 2.875 = 9.433629811 a = 9.433629811 Simplifying a = 9.433629811Subproblem 2
a + -2.875 = -6.558629811 Simplifying a + -2.875 = -6.558629811 Reorder the terms: -2.875 + a = -6.558629811 Solving -2.875 + a = -6.558629811 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + a = -6.558629811 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + a = -6.558629811 + 2.875 a = -6.558629811 + 2.875 Combine like terms: -6.558629811 + 2.875 = -3.683629811 a = -3.683629811 Simplifying a = -3.683629811Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.433629811, -3.683629811}
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