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Simplifying a2 + -20a + -53 = 9 Reorder the terms: -53 + -20a + a2 = 9 Solving -53 + -20a + a2 = 9 Solving for variable 'a'. Reorder the terms: -53 + -9 + -20a + a2 = 9 + -9 Combine like terms: -53 + -9 = -62 -62 + -20a + a2 = 9 + -9 Combine like terms: 9 + -9 = 0 -62 + -20a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + -20a + 62 + a2 = 0 + 62 Reorder the terms: -62 + 62 + -20a + a2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -20a + a2 = 0 + 62 -20a + a2 = 0 + 62 Combine like terms: 0 + 62 = 62 -20a + a2 = 62 The a term is -20a. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20a + 100 + a2 = 62 + 100 Reorder the terms: 100 + -20a + a2 = 62 + 100 Combine like terms: 62 + 100 = 162 100 + -20a + a2 = 162 Factor a perfect square on the left side: (a + -10)(a + -10) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (a + -10) equal to 12.727922061 and -12.727922061.Subproblem 1
a + -10 = 12.727922061 Simplifying a + -10 = 12.727922061 Reorder the terms: -10 + a = 12.727922061 Solving -10 + a = 12.727922061 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = 12.727922061 + 10 Combine like terms: -10 + 10 = 0 0 + a = 12.727922061 + 10 a = 12.727922061 + 10 Combine like terms: 12.727922061 + 10 = 22.727922061 a = 22.727922061 Simplifying a = 22.727922061Subproblem 2
a + -10 = -12.727922061 Simplifying a + -10 = -12.727922061 Reorder the terms: -10 + a = -12.727922061 Solving -10 + a = -12.727922061 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = -12.727922061 + 10 Combine like terms: -10 + 10 = 0 0 + a = -12.727922061 + 10 a = -12.727922061 + 10 Combine like terms: -12.727922061 + 10 = -2.727922061 a = -2.727922061 Simplifying a = -2.727922061Solution
The solution to the problem is based on the solutions from the subproblems. a = {22.727922061, -2.727922061}
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