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Simplifying 2x2 + 49x + -169 = 0 Reorder the terms: -169 + 49x + 2x2 = 0 Solving -169 + 49x + 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'. -84.5 + 24.5x + x2 = 0 Move the constant term to the right: Add '84.5' to each side of the equation. -84.5 + 24.5x + 84.5 + x2 = 0 + 84.5 Reorder the terms: -84.5 + 84.5 + 24.5x + x2 = 0 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + 24.5x + x2 = 0 + 84.5 24.5x + x2 = 0 + 84.5 Combine like terms: 0 + 84.5 = 84.5 24.5x + x2 = 84.5 The x term is 24.5x. Take half its coefficient (12.25). Square it (150.0625) and add it to both sides. Add '150.0625' to each side of the equation. 24.5x + 150.0625 + x2 = 84.5 + 150.0625 Reorder the terms: 150.0625 + 24.5x + x2 = 84.5 + 150.0625 Combine like terms: 84.5 + 150.0625 = 234.5625 150.0625 + 24.5x + x2 = 234.5625 Factor a perfect square on the left side: (x + 12.25)(x + 12.25) = 234.5625 Calculate the square root of the right side: 15.315433392 Break this problem into two subproblems by setting (x + 12.25) equal to 15.315433392 and -15.315433392.Subproblem 1
x + 12.25 = 15.315433392 Simplifying x + 12.25 = 15.315433392 Reorder the terms: 12.25 + x = 15.315433392 Solving 12.25 + x = 15.315433392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25' to each side of the equation. 12.25 + -12.25 + x = 15.315433392 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + x = 15.315433392 + -12.25 x = 15.315433392 + -12.25 Combine like terms: 15.315433392 + -12.25 = 3.065433392 x = 3.065433392 Simplifying x = 3.065433392Subproblem 2
x + 12.25 = -15.315433392 Simplifying x + 12.25 = -15.315433392 Reorder the terms: 12.25 + x = -15.315433392 Solving 12.25 + x = -15.315433392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25' to each side of the equation. 12.25 + -12.25 + x = -15.315433392 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + x = -15.315433392 + -12.25 x = -15.315433392 + -12.25 Combine like terms: -15.315433392 + -12.25 = -27.565433392 x = -27.565433392 Simplifying x = -27.565433392Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.065433392, -27.565433392}
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