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Simplifying 4a2 + -15 = 16a Reorder the terms: -15 + 4a2 = 16a Solving -15 + 4a2 = 16a Solving for variable 'a'. Reorder the terms: -15 + -16a + 4a2 = 16a + -16a Combine like terms: 16a + -16a = 0 -15 + -16a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -4a + a2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -4a + 3.75 + a2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -4a + a2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -4a + a2 = 0 + 3.75 -4a + a2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -4a + a2 = 3.75 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 3.75 + 4 Reorder the terms: 4 + -4a + a2 = 3.75 + 4 Combine like terms: 3.75 + 4 = 7.75 4 + -4a + a2 = 7.75 Factor a perfect square on the left side: (a + -2)(a + -2) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (a + -2) equal to 2.783882181 and -2.783882181.Subproblem 1
a + -2 = 2.783882181 Simplifying a + -2 = 2.783882181 Reorder the terms: -2 + a = 2.783882181 Solving -2 + a = 2.783882181 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 2.783882181 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.783882181 + 2 a = 2.783882181 + 2 Combine like terms: 2.783882181 + 2 = 4.783882181 a = 4.783882181 Simplifying a = 4.783882181Subproblem 2
a + -2 = -2.783882181 Simplifying a + -2 = -2.783882181 Reorder the terms: -2 + a = -2.783882181 Solving -2 + a = -2.783882181 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -2.783882181 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.783882181 + 2 a = -2.783882181 + 2 Combine like terms: -2.783882181 + 2 = -0.783882181 a = -0.783882181 Simplifying a = -0.783882181Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.783882181, -0.783882181}
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