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Simplifying -40a2 + 11a + 30 = 0 Reorder the terms: 30 + 11a + -40a2 = 0 Solving 30 + 11a + -40a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. -0.75 + -0.275a + a2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.275a + 0.75 + a2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.275a + a2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.275a + a2 = 0 + 0.75 -0.275a + a2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.275a + a2 = 0.75 The a term is -0.275a. Take half its coefficient (-0.1375). Square it (0.01890625) and add it to both sides. Add '0.01890625' to each side of the equation. -0.275a + 0.01890625 + a2 = 0.75 + 0.01890625 Reorder the terms: 0.01890625 + -0.275a + a2 = 0.75 + 0.01890625 Combine like terms: 0.75 + 0.01890625 = 0.76890625 0.01890625 + -0.275a + a2 = 0.76890625 Factor a perfect square on the left side: (a + -0.1375)(a + -0.1375) = 0.76890625 Calculate the square root of the right side: 0.876872995 Break this problem into two subproblems by setting (a + -0.1375) equal to 0.876872995 and -0.876872995.Subproblem 1
a + -0.1375 = 0.876872995 Simplifying a + -0.1375 = 0.876872995 Reorder the terms: -0.1375 + a = 0.876872995 Solving -0.1375 + a = 0.876872995 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1375' to each side of the equation. -0.1375 + 0.1375 + a = 0.876872995 + 0.1375 Combine like terms: -0.1375 + 0.1375 = 0.0000 0.0000 + a = 0.876872995 + 0.1375 a = 0.876872995 + 0.1375 Combine like terms: 0.876872995 + 0.1375 = 1.014372995 a = 1.014372995 Simplifying a = 1.014372995Subproblem 2
a + -0.1375 = -0.876872995 Simplifying a + -0.1375 = -0.876872995 Reorder the terms: -0.1375 + a = -0.876872995 Solving -0.1375 + a = -0.876872995 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1375' to each side of the equation. -0.1375 + 0.1375 + a = -0.876872995 + 0.1375 Combine like terms: -0.1375 + 0.1375 = 0.0000 0.0000 + a = -0.876872995 + 0.1375 a = -0.876872995 + 0.1375 Combine like terms: -0.876872995 + 0.1375 = -0.739372995 a = -0.739372995 Simplifying a = -0.739372995Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.014372995, -0.739372995}
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