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Simplifying 2x2 + 13x + 4 = 0 Reorder the terms: 4 + 13x + 2x2 = 0 Solving 4 + 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'. 2 + 6.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 6.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6.5x + x2 = 0 + -2 6.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 6.5x + x2 = -2 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 = -2 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -2 + 10.5625 Combine like terms: -2 + 10.5625 = 8.5625 10.5625 + 6.5x + x2 = 8.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (x + 3.25) equal to 2.926174978 and -2.926174978.Subproblem 1
x + 3.25 = 2.926174978 Simplifying x + 3.25 = 2.926174978 Reorder the terms: 3.25 + x = 2.926174978 Solving 3.25 + x = 2.926174978 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 = 2.926174978 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 2.926174978 + -3.25 x = 2.926174978 + -3.25 Combine like terms: 2.926174978 + -3.25 = -0.323825022 x = -0.323825022 Simplifying x = -0.323825022Subproblem 2
x + 3.25 = -2.926174978 Simplifying x + 3.25 = -2.926174978 Reorder the terms: 3.25 + x = -2.926174978 Solving 3.25 + x = -2.926174978 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 = -2.926174978 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -2.926174978 + -3.25 x = -2.926174978 + -3.25 Combine like terms: -2.926174978 + -3.25 = -6.176174978 x = -6.176174978 Simplifying x = -6.176174978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.323825022, -6.176174978}
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