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Simplifying 7a + -1a2 = -28 Solving 7a + -1a2 = -28 Solving for variable 'a'. Reorder the terms: 28 + 7a + -1a2 = -28 + 28 Combine like terms: -28 + 28 = 0 28 + 7a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + -7a + a2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -7a + 28 + a2 = 0 + 28 Reorder the terms: -28 + 28 + -7a + a2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -7a + a2 = 0 + 28 -7a + a2 = 0 + 28 Combine like terms: 0 + 28 = 28 -7a + a2 = 28 The a term is -7a. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7a + 12.25 + a2 = 28 + 12.25 Reorder the terms: 12.25 + -7a + a2 = 28 + 12.25 Combine like terms: 28 + 12.25 = 40.25 12.25 + -7a + a2 = 40.25 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (a + -3.5) equal to 6.34428877 and -6.34428877.Subproblem 1
a + -3.5 = 6.34428877 Simplifying a + -3.5 = 6.34428877 Reorder the terms: -3.5 + a = 6.34428877 Solving -3.5 + a = 6.34428877 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = 6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 6.34428877 + 3.5 a = 6.34428877 + 3.5 Combine like terms: 6.34428877 + 3.5 = 9.84428877 a = 9.84428877 Simplifying a = 9.84428877Subproblem 2
a + -3.5 = -6.34428877 Simplifying a + -3.5 = -6.34428877 Reorder the terms: -3.5 + a = -6.34428877 Solving -3.5 + a = -6.34428877 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = -6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -6.34428877 + 3.5 a = -6.34428877 + 3.5 Combine like terms: -6.34428877 + 3.5 = -2.84428877 a = -2.84428877 Simplifying a = -2.84428877Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.84428877, -2.84428877}
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