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Simplifying x2 + -1x + -49 = 0 Reorder the terms: -49 + -1x + x2 = 0 Solving -49 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -1x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -1x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -1x + x2 = 0 + 49 -1x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -1x + x2 = 49 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 49 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 49 + 0.25 Combine like terms: 49 + 0.25 = 49.25 0.25 + -1x + x2 = 49.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + -0.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + -0.5 = 7.017834424 Simplifying x + -0.5 = 7.017834424 Reorder the terms: -0.5 + x = 7.017834424 Solving -0.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 7.017834424 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.017834424 + 0.5 x = 7.017834424 + 0.5 Combine like terms: 7.017834424 + 0.5 = 7.517834424 x = 7.517834424 Simplifying x = 7.517834424Subproblem 2
x + -0.5 = -7.017834424 Simplifying x + -0.5 = -7.017834424 Reorder the terms: -0.5 + x = -7.017834424 Solving -0.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -7.017834424 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.017834424 + 0.5 x = -7.017834424 + 0.5 Combine like terms: -7.017834424 + 0.5 = -6.517834424 x = -6.517834424 Simplifying x = -6.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.517834424, -6.517834424}
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