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Simplifying 2x2 + -1x + -49 = 0 Reorder the terms: -49 + -1x + 2x2 = 0 Solving -49 + -1x + 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'. -24.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + -0.5x + 24.5 + x2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + -0.5x + x2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + -0.5x + x2 = 0 + 24.5 -0.5x + x2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 -0.5x + x2 = 24.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 24.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 24.5 + 0.0625 Combine like terms: 24.5 + 0.0625 = 24.5625 0.0625 + -0.5x + x2 = 24.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 24.5625 Calculate the square root of the right side: 4.9560569 Break this problem into two subproblems by setting (x + -0.25) equal to 4.9560569 and -4.9560569.Subproblem 1
x + -0.25 = 4.9560569 Simplifying x + -0.25 = 4.9560569 Reorder the terms: -0.25 + x = 4.9560569 Solving -0.25 + x = 4.9560569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 4.9560569 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 4.9560569 + 0.25 x = 4.9560569 + 0.25 Combine like terms: 4.9560569 + 0.25 = 5.2060569 x = 5.2060569 Simplifying x = 5.2060569Subproblem 2
x + -0.25 = -4.9560569 Simplifying x + -0.25 = -4.9560569 Reorder the terms: -0.25 + x = -4.9560569 Solving -0.25 + x = -4.9560569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -4.9560569 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -4.9560569 + 0.25 x = -4.9560569 + 0.25 Combine like terms: -4.9560569 + 0.25 = -4.7060569 x = -4.7060569 Simplifying x = -4.7060569Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.2060569, -4.7060569}
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