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Simplifying 2x2 + 13x + 12 = 0 Reorder the terms: 12 + 13x + 2x2 = 0 Solving 12 + 13x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6 + 6.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 6.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 6.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6.5x + x2 = 0 + -6 6.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 6.5x + x2 = -6 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -6 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -6 + 10.5625 Combine like terms: -6 + 10.5625 = 4.5625 10.5625 + 6.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + 3.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + 3.25 = 2.136000936 Simplifying x + 3.25 = 2.136000936 Reorder the terms: 3.25 + x = 2.136000936 Solving 3.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 2.136000936 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 2.136000936 + -3.25 x = 2.136000936 + -3.25 Combine like terms: 2.136000936 + -3.25 = -1.113999064 x = -1.113999064 Simplifying x = -1.113999064Subproblem 2
x + 3.25 = -2.136000936 Simplifying x + 3.25 = -2.136000936 Reorder the terms: 3.25 + x = -2.136000936 Solving 3.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -2.136000936 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -2.136000936 + -3.25 x = -2.136000936 + -3.25 Combine like terms: -2.136000936 + -3.25 = -5.386000936 x = -5.386000936 Simplifying x = -5.386000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.113999064, -5.386000936}
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