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Simplifying a2 + -24a + 120 = 0 Reorder the terms: 120 + -24a + a2 = 0 Solving 120 + -24a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + -24a + -120 + a2 = 0 + -120 Reorder the terms: 120 + -120 + -24a + a2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -24a + a2 = 0 + -120 -24a + a2 = 0 + -120 Combine like terms: 0 + -120 = -120 -24a + a2 = -120 The a term is -24a. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24a + 144 + a2 = -120 + 144 Reorder the terms: 144 + -24a + a2 = -120 + 144 Combine like terms: -120 + 144 = 24 144 + -24a + a2 = 24 Factor a perfect square on the left side: (a + -12)(a + -12) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (a + -12) equal to 4.898979486 and -4.898979486.Subproblem 1
a + -12 = 4.898979486 Simplifying a + -12 = 4.898979486 Reorder the terms: -12 + a = 4.898979486 Solving -12 + a = 4.898979486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + a = 4.898979486 + 12 Combine like terms: -12 + 12 = 0 0 + a = 4.898979486 + 12 a = 4.898979486 + 12 Combine like terms: 4.898979486 + 12 = 16.898979486 a = 16.898979486 Simplifying a = 16.898979486Subproblem 2
a + -12 = -4.898979486 Simplifying a + -12 = -4.898979486 Reorder the terms: -12 + a = -4.898979486 Solving -12 + a = -4.898979486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + a = -4.898979486 + 12 Combine like terms: -12 + 12 = 0 0 + a = -4.898979486 + 12 a = -4.898979486 + 12 Combine like terms: -4.898979486 + 12 = 7.101020514 a = 7.101020514 Simplifying a = 7.101020514Solution
The solution to the problem is based on the solutions from the subproblems. a = {16.898979486, 7.101020514}
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