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Simplifying x2 + -362x + -32320 = 0 Reorder the terms: -32320 + -362x + x2 = 0 Solving -32320 + -362x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32320' to each side of the equation. -32320 + -362x + 32320 + x2 = 0 + 32320 Reorder the terms: -32320 + 32320 + -362x + x2 = 0 + 32320 Combine like terms: -32320 + 32320 = 0 0 + -362x + x2 = 0 + 32320 -362x + x2 = 0 + 32320 Combine like terms: 0 + 32320 = 32320 -362x + x2 = 32320 The x term is -362x. Take half its coefficient (-181). Square it (32761) and add it to both sides. Add '32761' to each side of the equation. -362x + 32761 + x2 = 32320 + 32761 Reorder the terms: 32761 + -362x + x2 = 32320 + 32761 Combine like terms: 32320 + 32761 = 65081 32761 + -362x + x2 = 65081 Factor a perfect square on the left side: (x + -181)(x + -181) = 65081 Calculate the square root of the right side: 255.109780291 Break this problem into two subproblems by setting (x + -181) equal to 255.109780291 and -255.109780291.Subproblem 1
x + -181 = 255.109780291 Simplifying x + -181 = 255.109780291 Reorder the terms: -181 + x = 255.109780291 Solving -181 + x = 255.109780291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '181' to each side of the equation. -181 + 181 + x = 255.109780291 + 181 Combine like terms: -181 + 181 = 0 0 + x = 255.109780291 + 181 x = 255.109780291 + 181 Combine like terms: 255.109780291 + 181 = 436.109780291 x = 436.109780291 Simplifying x = 436.109780291Subproblem 2
x + -181 = -255.109780291 Simplifying x + -181 = -255.109780291 Reorder the terms: -181 + x = -255.109780291 Solving -181 + x = -255.109780291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '181' to each side of the equation. -181 + 181 + x = -255.109780291 + 181 Combine like terms: -181 + 181 = 0 0 + x = -255.109780291 + 181 x = -255.109780291 + 181 Combine like terms: -255.109780291 + 181 = -74.109780291 x = -74.109780291 Simplifying x = -74.109780291Solution
The solution to the problem is based on the solutions from the subproblems. x = {436.109780291, -74.109780291}
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