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Simplifying x2 + 138x + 500 = 0 Reorder the terms: 500 + 138x + x2 = 0 Solving 500 + 138x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + 138x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + 138x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + 138x + x2 = 0 + -500 138x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 138x + x2 = -500 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 = -500 + 4761 Reorder the terms: 4761 + 138x + x2 = -500 + 4761 Combine like terms: -500 + 4761 = 4261 4761 + 138x + x2 = 4261 Factor a perfect square on the left side: (x + 69)(x + 69) = 4261 Calculate the square root of the right side: 65.276335681 Break this problem into two subproblems by setting (x + 69) equal to 65.276335681 and -65.276335681.Subproblem 1
x + 69 = 65.276335681 Simplifying x + 69 = 65.276335681 Reorder the terms: 69 + x = 65.276335681 Solving 69 + x = 65.276335681 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 = 65.276335681 + -69 Combine like terms: 69 + -69 = 0 0 + x = 65.276335681 + -69 x = 65.276335681 + -69 Combine like terms: 65.276335681 + -69 = -3.723664319 x = -3.723664319 Simplifying x = -3.723664319Subproblem 2
x + 69 = -65.276335681 Simplifying x + 69 = -65.276335681 Reorder the terms: 69 + x = -65.276335681 Solving 69 + x = -65.276335681 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 = -65.276335681 + -69 Combine like terms: 69 + -69 = 0 0 + x = -65.276335681 + -69 x = -65.276335681 + -69 Combine like terms: -65.276335681 + -69 = -134.276335681 x = -134.276335681 Simplifying x = -134.276335681Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.723664319, -134.276335681}
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