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Simplifying a2 + -11a + 5 = 0 Reorder the terms: 5 + -11a + a2 = 0 Solving 5 + -11a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -11a + -5 + a2 = 0 + -5 Reorder the terms: 5 + -5 + -11a + a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -11a + a2 = 0 + -5 -11a + a2 = 0 + -5 Combine like terms: 0 + -5 = -5 -11a + a2 = -5 The a term is -11a. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11a + 30.25 + a2 = -5 + 30.25 Reorder the terms: 30.25 + -11a + a2 = -5 + 30.25 Combine like terms: -5 + 30.25 = 25.25 30.25 + -11a + a2 = 25.25 Factor a perfect square on the left side: (a + -5.5)(a + -5.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (a + -5.5) equal to 5.024937811 and -5.024937811.Subproblem 1
a + -5.5 = 5.024937811 Simplifying a + -5.5 = 5.024937811 Reorder the terms: -5.5 + a = 5.024937811 Solving -5.5 + a = 5.024937811 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = 5.024937811 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = 5.024937811 + 5.5 a = 5.024937811 + 5.5 Combine like terms: 5.024937811 + 5.5 = 10.524937811 a = 10.524937811 Simplifying a = 10.524937811Subproblem 2
a + -5.5 = -5.024937811 Simplifying a + -5.5 = -5.024937811 Reorder the terms: -5.5 + a = -5.024937811 Solving -5.5 + a = -5.024937811 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = -5.024937811 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = -5.024937811 + 5.5 a = -5.024937811 + 5.5 Combine like terms: -5.024937811 + 5.5 = 0.475062189 a = 0.475062189 Simplifying a = 0.475062189Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.524937811, 0.475062189}
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