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Simplifying a2 + -28a + 192 = 20 Reorder the terms: 192 + -28a + a2 = 20 Solving 192 + -28a + a2 = 20 Solving for variable 'a'. Reorder the terms: 192 + -20 + -28a + a2 = 20 + -20 Combine like terms: 192 + -20 = 172 172 + -28a + a2 = 20 + -20 Combine like terms: 20 + -20 = 0 172 + -28a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-172' to each side of the equation. 172 + -28a + -172 + a2 = 0 + -172 Reorder the terms: 172 + -172 + -28a + a2 = 0 + -172 Combine like terms: 172 + -172 = 0 0 + -28a + a2 = 0 + -172 -28a + a2 = 0 + -172 Combine like terms: 0 + -172 = -172 -28a + a2 = -172 The a term is -28a. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28a + 196 + a2 = -172 + 196 Reorder the terms: 196 + -28a + a2 = -172 + 196 Combine like terms: -172 + 196 = 24 196 + -28a + a2 = 24 Factor a perfect square on the left side: (a + -14)(a + -14) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (a + -14) equal to 4.898979486 and -4.898979486.Subproblem 1
a + -14 = 4.898979486 Simplifying a + -14 = 4.898979486 Reorder the terms: -14 + a = 4.898979486 Solving -14 + a = 4.898979486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + a = 4.898979486 + 14 Combine like terms: -14 + 14 = 0 0 + a = 4.898979486 + 14 a = 4.898979486 + 14 Combine like terms: 4.898979486 + 14 = 18.898979486 a = 18.898979486 Simplifying a = 18.898979486Subproblem 2
a + -14 = -4.898979486 Simplifying a + -14 = -4.898979486 Reorder the terms: -14 + a = -4.898979486 Solving -14 + a = -4.898979486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + a = -4.898979486 + 14 Combine like terms: -14 + 14 = 0 0 + a = -4.898979486 + 14 a = -4.898979486 + 14 Combine like terms: -4.898979486 + 14 = 9.101020514 a = 9.101020514 Simplifying a = 9.101020514Solution
The solution to the problem is based on the solutions from the subproblems. a = {18.898979486, 9.101020514}
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