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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 = 20.0625 10.5625 + 6.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + 3.25) equal to 4.479118217 and -4.479118217.Subproblem 1
x + 3.25 = 4.479118217 Simplifying x + 3.25 = 4.479118217 Reorder the terms: 3.25 + x = 4.479118217 Solving 3.25 + x = 4.479118217 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 = 4.479118217 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 4.479118217 + -3.25 x = 4.479118217 + -3.25 Combine like terms: 4.479118217 + -3.25 = 1.229118217 x = 1.229118217 Simplifying x = 1.229118217Subproblem 2
x + 3.25 = -4.479118217 Simplifying x + 3.25 = -4.479118217 Reorder the terms: 3.25 + x = -4.479118217 Solving 3.25 + x = -4.479118217 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 = -4.479118217 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -4.479118217 + -3.25 x = -4.479118217 + -3.25 Combine like terms: -4.479118217 + -3.25 = -7.729118217 x = -7.729118217 Simplifying x = -7.729118217Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.229118217, -7.729118217}
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