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Simplifying 7a2 + -30a + 4 = 0 Reorder the terms: 4 + -30a + 7a2 = 0 Solving 4 + -30a + 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'. 0.5714285714 + -4.285714286a + a2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -4.285714286a + -0.5714285714 + a2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -4.285714286a + a2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -4.285714286a + a2 = 0 + -0.5714285714 -4.285714286a + a2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -4.285714286a + a2 = -0.5714285714 The a term is -4.285714286a. Take half its coefficient (-2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. -4.285714286a + 4.591836735 + a2 = -0.5714285714 + 4.591836735 Reorder the terms: 4.591836735 + -4.285714286a + a2 = -0.5714285714 + 4.591836735 Combine like terms: -0.5714285714 + 4.591836735 = 4.0204081636 4.591836735 + -4.285714286a + a2 = 4.0204081636 Factor a perfect square on the left side: (a + -2.142857143)(a + -2.142857143) = 4.0204081636 Calculate the square root of the right side: 2.00509555 Break this problem into two subproblems by setting (a + -2.142857143) equal to 2.00509555 and -2.00509555.Subproblem 1
a + -2.142857143 = 2.00509555 Simplifying a + -2.142857143 = 2.00509555 Reorder the terms: -2.142857143 + a = 2.00509555 Solving -2.142857143 + a = 2.00509555 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + a = 2.00509555 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + a = 2.00509555 + 2.142857143 a = 2.00509555 + 2.142857143 Combine like terms: 2.00509555 + 2.142857143 = 4.147952693 a = 4.147952693 Simplifying a = 4.147952693Subproblem 2
a + -2.142857143 = -2.00509555 Simplifying a + -2.142857143 = -2.00509555 Reorder the terms: -2.142857143 + a = -2.00509555 Solving -2.142857143 + a = -2.00509555 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.142857143' to each side of the equation. -2.142857143 + 2.142857143 + a = -2.00509555 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + a = -2.00509555 + 2.142857143 a = -2.00509555 + 2.142857143 Combine like terms: -2.00509555 + 2.142857143 = 0.137761593 a = 0.137761593 Simplifying a = 0.137761593Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.147952693, 0.137761593}
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