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Simplifying 2x2 + 13x + 19 = 0 Reorder the terms: 19 + 13x + 2x2 = 0 Solving 19 + 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'. 9.5 + 6.5x + x2 = 0 Move the constant term to the right: Add '-9.5' to each side of the equation. 9.5 + 6.5x + -9.5 + x2 = 0 + -9.5 Reorder the terms: 9.5 + -9.5 + 6.5x + x2 = 0 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + 6.5x + x2 = 0 + -9.5 6.5x + x2 = 0 + -9.5 Combine like terms: 0 + -9.5 = -9.5 6.5x + x2 = -9.5 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 = -9.5 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -9.5 + 10.5625 Combine like terms: -9.5 + 10.5625 = 1.0625 10.5625 + 6.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 3.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 3.25 = 1.030776406 Simplifying x + 3.25 = 1.030776406 Reorder the terms: 3.25 + x = 1.030776406 Solving 3.25 + x = 1.030776406 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 = 1.030776406 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 1.030776406 + -3.25 x = 1.030776406 + -3.25 Combine like terms: 1.030776406 + -3.25 = -2.219223594 x = -2.219223594 Simplifying x = -2.219223594Subproblem 2
x + 3.25 = -1.030776406 Simplifying x + 3.25 = -1.030776406 Reorder the terms: 3.25 + x = -1.030776406 Solving 3.25 + x = -1.030776406 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 = -1.030776406 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -1.030776406 + -3.25 x = -1.030776406 + -3.25 Combine like terms: -1.030776406 + -3.25 = -4.280776406 x = -4.280776406 Simplifying x = -4.280776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.219223594, -4.280776406}
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