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Simplifying 2a2 + -15a + 4 = 0 Reorder the terms: 4 + -15a + 2a2 = 0 Solving 4 + -15a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -7.5a + a2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -7.5a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + -7.5a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7.5a + a2 = 0 + -2 -7.5a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7.5a + a2 = -2 The a term is -7.5a. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5a + 14.0625 + a2 = -2 + 14.0625 Reorder the terms: 14.0625 + -7.5a + a2 = -2 + 14.0625 Combine like terms: -2 + 14.0625 = 12.0625 14.0625 + -7.5a + a2 = 12.0625 Factor a perfect square on the left side: (a + -3.75)(a + -3.75) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (a + -3.75) equal to 3.473110997 and -3.473110997.Subproblem 1
a + -3.75 = 3.473110997 Simplifying a + -3.75 = 3.473110997 Reorder the terms: -3.75 + a = 3.473110997 Solving -3.75 + a = 3.473110997 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + a = 3.473110997 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + a = 3.473110997 + 3.75 a = 3.473110997 + 3.75 Combine like terms: 3.473110997 + 3.75 = 7.223110997 a = 7.223110997 Simplifying a = 7.223110997Subproblem 2
a + -3.75 = -3.473110997 Simplifying a + -3.75 = -3.473110997 Reorder the terms: -3.75 + a = -3.473110997 Solving -3.75 + a = -3.473110997 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + a = -3.473110997 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + a = -3.473110997 + 3.75 a = -3.473110997 + 3.75 Combine like terms: -3.473110997 + 3.75 = 0.276889003 a = 0.276889003 Simplifying a = 0.276889003Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.223110997, 0.276889003}
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