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Simplifying 4a2 + a + -15 = 0 Reorder the terms: -15 + a + 4a2 = 0 Solving -15 + a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 0.25a + a2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 0.25a + 3.75 + a2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 0.25a + a2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 0.25a + a2 = 0 + 3.75 0.25a + a2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 0.25a + a2 = 3.75 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25a + 0.25 + a2 = 3.75 + 0.25 Reorder the terms: 0.25 + 0.25a + a2 = 3.75 + 0.25 Combine like terms: 3.75 + 0.25 = 4 0.25 + 0.25a + a2 = 4 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (a + 0.5) equal to 2 and -2.Subproblem 1
a + 0.5 = 2 Simplifying a + 0.5 = 2 Reorder the terms: 0.5 + a = 2 Solving 0.5 + a = 2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 2 + -0.5 a = 2 + -0.5 Combine like terms: 2 + -0.5 = 1.5 a = 1.5 Simplifying a = 1.5Subproblem 2
a + 0.5 = -2 Simplifying a + 0.5 = -2 Reorder the terms: 0.5 + a = -2 Solving 0.5 + a = -2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -2 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -2 + -0.5 a = -2 + -0.5 Combine like terms: -2 + -0.5 = -2.5 a = -2.5 Simplifying a = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.5, -2.5}
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