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Simplifying x2 + -138x + 540 = 0 Reorder the terms: 540 + -138x + x2 = 0 Solving 540 + -138x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-540' to each side of the equation. 540 + -138x + -540 + x2 = 0 + -540 Reorder the terms: 540 + -540 + -138x + x2 = 0 + -540 Combine like terms: 540 + -540 = 0 0 + -138x + x2 = 0 + -540 -138x + x2 = 0 + -540 Combine like terms: 0 + -540 = -540 -138x + x2 = -540 The x term is -138x. Take half its coefficient (-69). Square it (4761) and add it to both sides. Add '4761' to each side of the equation. -138x + 4761 + x2 = -540 + 4761 Reorder the terms: 4761 + -138x + x2 = -540 + 4761 Combine like terms: -540 + 4761 = 4221 4761 + -138x + x2 = 4221 Factor a perfect square on the left side: (x + -69)(x + -69) = 4221 Calculate the square root of the right side: 64.969223483 Break this problem into two subproblems by setting (x + -69) equal to 64.969223483 and -64.969223483.Subproblem 1
x + -69 = 64.969223483 Simplifying x + -69 = 64.969223483 Reorder the terms: -69 + x = 64.969223483 Solving -69 + x = 64.969223483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '69' to each side of the equation. -69 + 69 + x = 64.969223483 + 69 Combine like terms: -69 + 69 = 0 0 + x = 64.969223483 + 69 x = 64.969223483 + 69 Combine like terms: 64.969223483 + 69 = 133.969223483 x = 133.969223483 Simplifying x = 133.969223483Subproblem 2
x + -69 = -64.969223483 Simplifying x + -69 = -64.969223483 Reorder the terms: -69 + x = -64.969223483 Solving -69 + x = -64.969223483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '69' to each side of the equation. -69 + 69 + x = -64.969223483 + 69 Combine like terms: -69 + 69 = 0 0 + x = -64.969223483 + 69 x = -64.969223483 + 69 Combine like terms: -64.969223483 + 69 = 4.030776517 x = 4.030776517 Simplifying x = 4.030776517Solution
The solution to the problem is based on the solutions from the subproblems. x = {133.969223483, 4.030776517}
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