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Simplifying 0 = x2 + x + -54.598 Reorder the terms: 0 = -54.598 + x + x2 Solving 0 = -54.598 + x + x2 Solving for variable 'x'. Combine like terms: 0 + 54.598 = 54.598 54.598 + -1x + -1x2 = -54.598 + x + x2 + 54.598 + -1x + -1x2 Reorder the terms: 54.598 + -1x + -1x2 = -54.598 + 54.598 + x + -1x + x2 + -1x2 Combine like terms: -54.598 + 54.598 = 0.000 54.598 + -1x + -1x2 = 0.000 + x + -1x + x2 + -1x2 54.598 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 54.598 + -1x + -1x2 = 0 + x2 + -1x2 54.598 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 54.598 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -54.598 + x + x2 = 0 Move the constant term to the right: Add '54.598' to each side of the equation. -54.598 + x + 54.598 + x2 = 0 + 54.598 Reorder the terms: -54.598 + 54.598 + x + x2 = 0 + 54.598 Combine like terms: -54.598 + 54.598 = 0.000 0.000 + x + x2 = 0 + 54.598 x + x2 = 0 + 54.598 Combine like terms: 0 + 54.598 = 54.598 x + x2 = 54.598 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. + 0.25 + x2 = 54.598 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 54.598 + 0.25 Combine like terms: 54.598 + 0.25 = 54.848 1.25 + x2 = 54.848 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 54.848 Calculate the square root of the right side: 7.405943559 Break this problem into two subproblems by setting (x + 0.5) equal to 7.405943559 and -7.405943559.Subproblem 1
x + 0.5 = 7.405943559 Simplifying x + 0.5 = 7.405943559 Reorder the terms: 0.5 + x = 7.405943559 Solving 0.5 + x = 7.405943559 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 = 7.405943559 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.405943559 + -0.5 x = 7.405943559 + -0.5 Combine like terms: 7.405943559 + -0.5 = 6.905943559 x = 6.905943559 Simplifying x = 6.905943559Subproblem 2
x + 0.5 = -7.405943559 Simplifying x + 0.5 = -7.405943559 Reorder the terms: 0.5 + x = -7.405943559 Solving 0.5 + x = -7.405943559 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 = -7.405943559 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.405943559 + -0.5 x = -7.405943559 + -0.5 Combine like terms: -7.405943559 + -0.5 = -7.905943559 x = -7.905943559 Simplifying x = -7.905943559Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.905943559, -7.905943559}
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