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Simplifying 2x2 + 13x + -168 = 0 Reorder the terms: -168 + 13x + 2x2 = 0 Solving -168 + 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'. -84 + 6.5x + x2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + 6.5x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 6.5x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 6.5x + x2 = 0 + 84 6.5x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 6.5x + x2 = 84 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 = 84 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 84 + 10.5625 Combine like terms: 84 + 10.5625 = 94.5625 10.5625 + 6.5x + x2 = 94.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 94.5625 Calculate the square root of the right side: 9.724325169 Break this problem into two subproblems by setting (x + 3.25) equal to 9.724325169 and -9.724325169.Subproblem 1
x + 3.25 = 9.724325169 Simplifying x + 3.25 = 9.724325169 Reorder the terms: 3.25 + x = 9.724325169 Solving 3.25 + x = 9.724325169 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 = 9.724325169 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 9.724325169 + -3.25 x = 9.724325169 + -3.25 Combine like terms: 9.724325169 + -3.25 = 6.474325169 x = 6.474325169 Simplifying x = 6.474325169Subproblem 2
x + 3.25 = -9.724325169 Simplifying x + 3.25 = -9.724325169 Reorder the terms: 3.25 + x = -9.724325169 Solving 3.25 + x = -9.724325169 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 = -9.724325169 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -9.724325169 + -3.25 x = -9.724325169 + -3.25 Combine like terms: -9.724325169 + -3.25 = -12.974325169 x = -12.974325169 Simplifying x = -12.974325169Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.474325169, -12.974325169}
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