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Simplifying 2a(a + -4) = 30 Reorder the terms: 2a(-4 + a) = 30 (-4 * 2a + a * 2a) = 30 (-8a + 2a2) = 30 Solving -8a + 2a2 = 30 Solving for variable 'a'. Reorder the terms: -30 + -8a + 2a2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -8a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -4a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -4a + a2)' equal to zero and attempt to solve: Simplifying -15 + -4a + a2 = 0 Solving -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}Solution
a = {6.358898944, -2.358898944}
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