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Simplifying (x) = x2 + 6x + -54 x = x2 + 6x + -54 Reorder the terms: x = -54 + 6x + x2 Solving x = -54 + 6x + x2 Solving for variable 'x'. Reorder the terms: 54 + x + -6x + -1x2 = -54 + 6x + x2 + 54 + -6x + -1x2 Combine like terms: x + -6x = -5x 54 + -5x + -1x2 = -54 + 6x + x2 + 54 + -6x + -1x2 Reorder the terms: 54 + -5x + -1x2 = -54 + 54 + 6x + -6x + x2 + -1x2 Combine like terms: -54 + 54 = 0 54 + -5x + -1x2 = 0 + 6x + -6x + x2 + -1x2 54 + -5x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 54 + -5x + -1x2 = 0 + x2 + -1x2 54 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 54 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -54 + 5x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 5x + x2 = 0 + 54 5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 5x + x2 = 54 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 54 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 54 + 6.25 Combine like terms: 54 + 6.25 = 60.25 6.25 + 5x + x2 = 60.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + 2.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + 2.5 = 7.762087348 Simplifying x + 2.5 = 7.762087348 Reorder the terms: 2.5 + x = 7.762087348 Solving 2.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.762087348 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.762087348 + -2.5 x = 7.762087348 + -2.5 Combine like terms: 7.762087348 + -2.5 = 5.262087348 x = 5.262087348 Simplifying x = 5.262087348Subproblem 2
x + 2.5 = -7.762087348 Simplifying x + 2.5 = -7.762087348 Reorder the terms: 2.5 + x = -7.762087348 Solving 2.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.762087348 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.762087348 + -2.5 x = -7.762087348 + -2.5 Combine like terms: -7.762087348 + -2.5 = -10.262087348 x = -10.262087348 Simplifying x = -10.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.262087348, -10.262087348}
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