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Simplifying 4a2 + 7a = 24 Reorder the terms: 7a + 4a2 = 24 Solving 7a + 4a2 = 24 Solving for variable 'a'. Reorder the terms: -24 + 7a + 4a2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 7a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6 + 1.75a + a2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.75a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + 1.75a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.75a + a2 = 0 + 6 1.75a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.75a + a2 = 6 The a term is 1.75a. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75a + 0.765625 + a2 = 6 + 0.765625 Reorder the terms: 0.765625 + 1.75a + a2 = 6 + 0.765625 Combine like terms: 6 + 0.765625 = 6.765625 0.765625 + 1.75a + a2 = 6.765625 Factor a perfect square on the left side: (a + 0.875)(a + 0.875) = 6.765625 Calculate the square root of the right side: 2.601081506 Break this problem into two subproblems by setting (a + 0.875) equal to 2.601081506 and -2.601081506.Subproblem 1
a + 0.875 = 2.601081506 Simplifying a + 0.875 = 2.601081506 Reorder the terms: 0.875 + a = 2.601081506 Solving 0.875 + a = 2.601081506 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + a = 2.601081506 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + a = 2.601081506 + -0.875 a = 2.601081506 + -0.875 Combine like terms: 2.601081506 + -0.875 = 1.726081506 a = 1.726081506 Simplifying a = 1.726081506Subproblem 2
a + 0.875 = -2.601081506 Simplifying a + 0.875 = -2.601081506 Reorder the terms: 0.875 + a = -2.601081506 Solving 0.875 + a = -2.601081506 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + a = -2.601081506 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + a = -2.601081506 + -0.875 a = -2.601081506 + -0.875 Combine like terms: -2.601081506 + -0.875 = -3.476081506 a = -3.476081506 Simplifying a = -3.476081506Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.726081506, -3.476081506}
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