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Simplifying 7a2 + 53a = 28 Reorder the terms: 53a + 7a2 = 28 Solving 53a + 7a2 = 28 Solving for variable 'a'. Reorder the terms: -28 + 53a + 7a2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 53a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4 + 7.571428571a + a2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 7.571428571a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + 7.571428571a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7.571428571a + a2 = 0 + 4 7.571428571a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 7.571428571a + a2 = 4 The a term is 7.571428571a. Take half its coefficient (3.785714286). Square it (14.33163266) and add it to both sides. Add '14.33163266' to each side of the equation. 7.571428571a + 14.33163266 + a2 = 4 + 14.33163266 Reorder the terms: 14.33163266 + 7.571428571a + a2 = 4 + 14.33163266 Combine like terms: 4 + 14.33163266 = 18.33163266 14.33163266 + 7.571428571a + a2 = 18.33163266 Factor a perfect square on the left side: (a + 3.785714286)(a + 3.785714286) = 18.33163266 Calculate the square root of the right side: 4.281545592 Break this problem into two subproblems by setting (a + 3.785714286) equal to 4.281545592 and -4.281545592.Subproblem 1
a + 3.785714286 = 4.281545592 Simplifying a + 3.785714286 = 4.281545592 Reorder the terms: 3.785714286 + a = 4.281545592 Solving 3.785714286 + a = 4.281545592 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.785714286' to each side of the equation. 3.785714286 + -3.785714286 + a = 4.281545592 + -3.785714286 Combine like terms: 3.785714286 + -3.785714286 = 0.000000000 0.000000000 + a = 4.281545592 + -3.785714286 a = 4.281545592 + -3.785714286 Combine like terms: 4.281545592 + -3.785714286 = 0.495831306 a = 0.495831306 Simplifying a = 0.495831306Subproblem 2
a + 3.785714286 = -4.281545592 Simplifying a + 3.785714286 = -4.281545592 Reorder the terms: 3.785714286 + a = -4.281545592 Solving 3.785714286 + a = -4.281545592 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.785714286' to each side of the equation. 3.785714286 + -3.785714286 + a = -4.281545592 + -3.785714286 Combine like terms: 3.785714286 + -3.785714286 = 0.000000000 0.000000000 + a = -4.281545592 + -3.785714286 a = -4.281545592 + -3.785714286 Combine like terms: -4.281545592 + -3.785714286 = -8.067259878 a = -8.067259878 Simplifying a = -8.067259878Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.495831306, -8.067259878}
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