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Simplifying x2 + 5x + -54 = 43 Reorder the terms: -54 + 5x + x2 = 43 Solving -54 + 5x + x2 = 43 Solving for variable 'x'. Reorder the terms: -54 + -43 + 5x + x2 = 43 + -43 Combine like terms: -54 + -43 = -97 -97 + 5x + x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -97 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + 5x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + 5x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + 5x + x2 = 0 + 97 5x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 5x + x2 = 97 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 = 97 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 97 + 6.25 Combine like terms: 97 + 6.25 = 103.25 6.25 + 5x + x2 = 103.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 103.25 Calculate the square root of the right side: 10.161200716 Break this problem into two subproblems by setting (x + 2.5) equal to 10.161200716 and -10.161200716.Subproblem 1
x + 2.5 = 10.161200716 Simplifying x + 2.5 = 10.161200716 Reorder the terms: 2.5 + x = 10.161200716 Solving 2.5 + x = 10.161200716 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 = 10.161200716 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.161200716 + -2.5 x = 10.161200716 + -2.5 Combine like terms: 10.161200716 + -2.5 = 7.661200716 x = 7.661200716 Simplifying x = 7.661200716Subproblem 2
x + 2.5 = -10.161200716 Simplifying x + 2.5 = -10.161200716 Reorder the terms: 2.5 + x = -10.161200716 Solving 2.5 + x = -10.161200716 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 = -10.161200716 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.161200716 + -2.5 x = -10.161200716 + -2.5 Combine like terms: -10.161200716 + -2.5 = -12.661200716 x = -12.661200716 Simplifying x = -12.661200716Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.661200716, -12.661200716}
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