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Simplifying a2 + -40a + -704 = 0 Reorder the terms: -704 + -40a + a2 = 0 Solving -704 + -40a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '704' to each side of the equation. -704 + -40a + 704 + a2 = 0 + 704 Reorder the terms: -704 + 704 + -40a + a2 = 0 + 704 Combine like terms: -704 + 704 = 0 0 + -40a + a2 = 0 + 704 -40a + a2 = 0 + 704 Combine like terms: 0 + 704 = 704 -40a + a2 = 704 The a term is -40a. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40a + 400 + a2 = 704 + 400 Reorder the terms: 400 + -40a + a2 = 704 + 400 Combine like terms: 704 + 400 = 1104 400 + -40a + a2 = 1104 Factor a perfect square on the left side: (a + -20)(a + -20) = 1104 Calculate the square root of the right side: 33.226495452 Break this problem into two subproblems by setting (a + -20) equal to 33.226495452 and -33.226495452.Subproblem 1
a + -20 = 33.226495452 Simplifying a + -20 = 33.226495452 Reorder the terms: -20 + a = 33.226495452 Solving -20 + a = 33.226495452 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = 33.226495452 + 20 Combine like terms: -20 + 20 = 0 0 + a = 33.226495452 + 20 a = 33.226495452 + 20 Combine like terms: 33.226495452 + 20 = 53.226495452 a = 53.226495452 Simplifying a = 53.226495452Subproblem 2
a + -20 = -33.226495452 Simplifying a + -20 = -33.226495452 Reorder the terms: -20 + a = -33.226495452 Solving -20 + a = -33.226495452 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = -33.226495452 + 20 Combine like terms: -20 + 20 = 0 0 + a = -33.226495452 + 20 a = -33.226495452 + 20 Combine like terms: -33.226495452 + 20 = -13.226495452 a = -13.226495452 Simplifying a = -13.226495452Solution
The solution to the problem is based on the solutions from the subproblems. a = {53.226495452, -13.226495452}
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