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Simplifying x2 + 160x + 420 = 0 Reorder the terms: 420 + 160x + x2 = 0 Solving 420 + 160x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-420' to each side of the equation. 420 + 160x + -420 + x2 = 0 + -420 Reorder the terms: 420 + -420 + 160x + x2 = 0 + -420 Combine like terms: 420 + -420 = 0 0 + 160x + x2 = 0 + -420 160x + x2 = 0 + -420 Combine like terms: 0 + -420 = -420 160x + x2 = -420 The x term is 160x. Take half its coefficient (80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. 160x + 6400 + x2 = -420 + 6400 Reorder the terms: 6400 + 160x + x2 = -420 + 6400 Combine like terms: -420 + 6400 = 5980 6400 + 160x + x2 = 5980 Factor a perfect square on the left side: (x + 80)(x + 80) = 5980 Calculate the square root of the right side: 77.330459717 Break this problem into two subproblems by setting (x + 80) equal to 77.330459717 and -77.330459717.Subproblem 1
x + 80 = 77.330459717 Simplifying x + 80 = 77.330459717 Reorder the terms: 80 + x = 77.330459717 Solving 80 + x = 77.330459717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = 77.330459717 + -80 Combine like terms: 80 + -80 = 0 0 + x = 77.330459717 + -80 x = 77.330459717 + -80 Combine like terms: 77.330459717 + -80 = -2.669540283 x = -2.669540283 Simplifying x = -2.669540283Subproblem 2
x + 80 = -77.330459717 Simplifying x + 80 = -77.330459717 Reorder the terms: 80 + x = -77.330459717 Solving 80 + x = -77.330459717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = -77.330459717 + -80 Combine like terms: 80 + -80 = 0 0 + x = -77.330459717 + -80 x = -77.330459717 + -80 Combine like terms: -77.330459717 + -80 = -157.330459717 x = -157.330459717 Simplifying x = -157.330459717Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.669540283, -157.330459717}
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