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Simplifying a2 + -80a + 1581 = 0 Reorder the terms: 1581 + -80a + a2 = 0 Solving 1581 + -80a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-1581' to each side of the equation. 1581 + -80a + -1581 + a2 = 0 + -1581 Reorder the terms: 1581 + -1581 + -80a + a2 = 0 + -1581 Combine like terms: 1581 + -1581 = 0 0 + -80a + a2 = 0 + -1581 -80a + a2 = 0 + -1581 Combine like terms: 0 + -1581 = -1581 -80a + a2 = -1581 The a term is -80a. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80a + 1600 + a2 = -1581 + 1600 Reorder the terms: 1600 + -80a + a2 = -1581 + 1600 Combine like terms: -1581 + 1600 = 19 1600 + -80a + a2 = 19 Factor a perfect square on the left side: (a + -40)(a + -40) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (a + -40) equal to 4.358898944 and -4.358898944.Subproblem 1
a + -40 = 4.358898944 Simplifying a + -40 = 4.358898944 Reorder the terms: -40 + a = 4.358898944 Solving -40 + a = 4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + a = 4.358898944 + 40 Combine like terms: -40 + 40 = 0 0 + a = 4.358898944 + 40 a = 4.358898944 + 40 Combine like terms: 4.358898944 + 40 = 44.358898944 a = 44.358898944 Simplifying a = 44.358898944Subproblem 2
a + -40 = -4.358898944 Simplifying a + -40 = -4.358898944 Reorder the terms: -40 + a = -4.358898944 Solving -40 + a = -4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + a = -4.358898944 + 40 Combine like terms: -40 + 40 = 0 0 + a = -4.358898944 + 40 a = -4.358898944 + 40 Combine like terms: -4.358898944 + 40 = 35.641101056 a = 35.641101056 Simplifying a = 35.641101056Solution
The solution to the problem is based on the solutions from the subproblems. a = {44.358898944, 35.641101056}
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