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Simplifying (0.12x2) + 1.56x + 4.81 = 0 Reorder the terms: 4.81 + 1.56x + (0.12x2) = 0 Solving 4.81 + 1.56x + (0.12x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.12 the coefficient of the squared term: Divide each side by '0.12'. 40.08333333 + 13x + x2 = 0 Move the constant term to the right: Add '-40.08333333' to each side of the equation. 40.08333333 + 13x + -40.08333333 + x2 = 0 + -40.08333333 Reorder the terms: 40.08333333 + -40.08333333 + 13x + x2 = 0 + -40.08333333 Combine like terms: 40.08333333 + -40.08333333 = 0.00000000 0.00000000 + 13x + x2 = 0 + -40.08333333 13x + x2 = 0 + -40.08333333 Combine like terms: 0 + -40.08333333 = -40.08333333 13x + x2 = -40.08333333 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -40.08333333 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -40.08333333 + 42.25 Combine like terms: -40.08333333 + 42.25 = 2.16666667 42.25 + 13x + x2 = 2.16666667 Factor a perfect square on the left side: ((x) + 6.5)((x) + 6.5) = 2.16666667 Calculate the square root of the right side: 1.471960146 Break this problem into two subproblems by setting ((x) + 6.5) equal to 1.471960146 and -1.471960146.Subproblem 1
(x) + 6.5 = 1.471960146 Simplifying (x) + 6.5 = 1.471960146 x + 6.5 = 1.471960146 Reorder the terms: 6.5 + x = 1.471960146 Solving 6.5 + x = 1.471960146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 1.471960146 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 1.471960146 + -6.5 x = 1.471960146 + -6.5 Combine like terms: 1.471960146 + -6.5 = -5.028039854 x = -5.028039854 Simplifying x = -5.028039854Subproblem 2
(x) + 6.5 = -1.471960146 Simplifying (x) + 6.5 = -1.471960146 x + 6.5 = -1.471960146 Reorder the terms: 6.5 + x = -1.471960146 Solving 6.5 + x = -1.471960146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -1.471960146 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -1.471960146 + -6.5 x = -1.471960146 + -6.5 Combine like terms: -1.471960146 + -6.5 = -7.971960146 x = -7.971960146 Simplifying x = -7.971960146Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.028039854, -7.971960146}
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