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Simplifying a2 + -15 = 4a Reorder the terms: -15 + a2 = 4a Solving -15 + a2 = 4a Solving for variable 'a'. Reorder the terms: -15 + -4a + a2 = 4a + -4a Combine like terms: 4a + -4a = 0 -15 + -4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -4a + 15 + a2 = 0 + 15 Reorder the terms: -15 + 15 + -4a + a2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4a + a2 = 0 + 15 -4a + a2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4a + a2 = 15 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 = 15 + 4 Reorder the terms: 4 + -4a + a2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + -4a + a2 = 19 Factor a perfect square on the left side: (a + -2)(a + -2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (a + -2) equal to 4.358898944 and -4.358898944.Subproblem 1
a + -2 = 4.358898944 Simplifying a + -2 = 4.358898944 Reorder the terms: -2 + a = 4.358898944 Solving -2 + a = 4.358898944 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 = 4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + a = 4.358898944 + 2 a = 4.358898944 + 2 Combine like terms: 4.358898944 + 2 = 6.358898944 a = 6.358898944 Simplifying a = 6.358898944Subproblem 2
a + -2 = -4.358898944 Simplifying a + -2 = -4.358898944 Reorder the terms: -2 + a = -4.358898944 Solving -2 + a = -4.358898944 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 = -4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + a = -4.358898944 + 2 a = -4.358898944 + 2 Combine like terms: -4.358898944 + 2 = -2.358898944 a = -2.358898944 Simplifying a = -2.358898944Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.358898944, -2.358898944}
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