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Simplifying 2a2 + a = 7 Reorder the terms: a + 2a2 = 7 Solving a + 2a2 = 7 Solving for variable 'a'. Reorder the terms: -7 + a + 2a2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 0.5a + a2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 0.5a + 3.5 + a2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 0.5a + a2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 0.5a + a2 = 0 + 3.5 0.5a + a2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 0.5a + a2 = 3.5 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. 0.5a + 0.25 + a2 = 3.5 + 0.25 Reorder the terms: 0.25 + 0.5a + a2 = 3.5 + 0.25 Combine like terms: 3.5 + 0.25 = 3.75 0.25 + 0.5a + a2 = 3.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (a + 0.5) equal to 1.936491673 and -1.936491673.Subproblem 1
a + 0.5 = 1.936491673 Simplifying a + 0.5 = 1.936491673 Reorder the terms: 0.5 + a = 1.936491673 Solving 0.5 + a = 1.936491673 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 = 1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 1.936491673 + -0.5 a = 1.936491673 + -0.5 Combine like terms: 1.936491673 + -0.5 = 1.436491673 a = 1.436491673 Simplifying a = 1.436491673Subproblem 2
a + 0.5 = -1.936491673 Simplifying a + 0.5 = -1.936491673 Reorder the terms: 0.5 + a = -1.936491673 Solving 0.5 + a = -1.936491673 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 = -1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -1.936491673 + -0.5 a = -1.936491673 + -0.5 Combine like terms: -1.936491673 + -0.5 = -2.436491673 a = -2.436491673 Simplifying a = -2.436491673Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.436491673, -2.436491673}
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