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Simplifying x + 1 + -4 = x2 + -49 Reorder the terms: 1 + -4 + x = x2 + -49 Combine like terms: 1 + -4 = -3 -3 + x = x2 + -49 Reorder the terms: -3 + x = -49 + x2 Solving -3 + x = -49 + x2 Solving for variable 'x'. Reorder the terms: -3 + 49 + x + -1x2 = -49 + x2 + 49 + -1x2 Combine like terms: -3 + 49 = 46 46 + x + -1x2 = -49 + x2 + 49 + -1x2 Reorder the terms: 46 + x + -1x2 = -49 + 49 + x2 + -1x2 Combine like terms: -49 + 49 = 0 46 + x + -1x2 = 0 + x2 + -1x2 46 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 46 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -46 + -1x + x2 = 0 Move the constant term to the right: Add '46' to each side of the equation. -46 + -1x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + -1x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -1x + x2 = 0 + 46 -1x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 -1x + x2 = 46 The x term is x. 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 = 46 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 46 + 0.25 Combine like terms: 46 + 0.25 = 46.25 0.25 + -1x + x2 = 46.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + 0.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + 0.5 = 6.800735254 Simplifying x + 0.5 = 6.800735254 Reorder the terms: 0.5 + x = 6.800735254 Solving 0.5 + x = 6.800735254 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 = 6.800735254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.800735254 + -0.5 x = 6.800735254 + -0.5 Combine like terms: 6.800735254 + -0.5 = 6.300735254 x = 6.300735254 Simplifying x = 6.300735254Subproblem 2
x + 0.5 = -6.800735254 Simplifying x + 0.5 = -6.800735254 Reorder the terms: 0.5 + x = -6.800735254 Solving 0.5 + x = -6.800735254 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 = -6.800735254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.800735254 + -0.5 x = -6.800735254 + -0.5 Combine like terms: -6.800735254 + -0.5 = -7.300735254 x = -7.300735254 Simplifying x = -7.300735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.300735254, -7.300735254}
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