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Simplifying 7a2 + -49a + -8 = 0 Reorder the terms: -8 + -49a + 7a2 = 0 Solving -8 + -49a + 7a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -7a + a2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -7a + 1.142857143 + a2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -7a + a2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -7a + a2 = 0 + 1.142857143 -7a + a2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -7a + a2 = 1.142857143 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 = 1.142857143 + 12.25 Reorder the terms: 12.25 + -7a + a2 = 1.142857143 + 12.25 Combine like terms: 1.142857143 + 12.25 = 13.392857143 12.25 + -7a + a2 = 13.392857143 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 13.392857143 Calculate the square root of the right side: 3.659625274 Break this problem into two subproblems by setting (a + -3.5) equal to 3.659625274 and -3.659625274.Subproblem 1
a + -3.5 = 3.659625274 Simplifying a + -3.5 = 3.659625274 Reorder the terms: -3.5 + a = 3.659625274 Solving -3.5 + a = 3.659625274 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 = 3.659625274 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 3.659625274 + 3.5 a = 3.659625274 + 3.5 Combine like terms: 3.659625274 + 3.5 = 7.159625274 a = 7.159625274 Simplifying a = 7.159625274Subproblem 2
a + -3.5 = -3.659625274 Simplifying a + -3.5 = -3.659625274 Reorder the terms: -3.5 + a = -3.659625274 Solving -3.5 + a = -3.659625274 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 = -3.659625274 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -3.659625274 + 3.5 a = -3.659625274 + 3.5 Combine like terms: -3.659625274 + 3.5 = -0.159625274 a = -0.159625274 Simplifying a = -0.159625274Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.159625274, -0.159625274}
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