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Simplifying 2x2 + 13x + -8 = 0 Reorder the terms: -8 + 13x + 2x2 = 0 Solving -8 + 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'. -4 + 6.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 6.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 6.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6.5x + x2 = 0 + 4 6.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 6.5x + x2 = 4 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 = 4 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 4 + 10.5625 Combine like terms: 4 + 10.5625 = 14.5625 10.5625 + 6.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + 3.25) equal to 3.816084381 and -3.816084381.Subproblem 1
x + 3.25 = 3.816084381 Simplifying x + 3.25 = 3.816084381 Reorder the terms: 3.25 + x = 3.816084381 Solving 3.25 + x = 3.816084381 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 = 3.816084381 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.816084381 + -3.25 x = 3.816084381 + -3.25 Combine like terms: 3.816084381 + -3.25 = 0.566084381 x = 0.566084381 Simplifying x = 0.566084381Subproblem 2
x + 3.25 = -3.816084381 Simplifying x + 3.25 = -3.816084381 Reorder the terms: 3.25 + x = -3.816084381 Solving 3.25 + x = -3.816084381 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 = -3.816084381 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.816084381 + -3.25 x = -3.816084381 + -3.25 Combine like terms: -3.816084381 + -3.25 = -7.066084381 x = -7.066084381 Simplifying x = -7.066084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.566084381, -7.066084381}
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