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Simplifying x2 + 320x + -320 = 0 Reorder the terms: -320 + 320x + x2 = 0 Solving -320 + 320x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '320' to each side of the equation. -320 + 320x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + 320x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 320x + x2 = 0 + 320 320x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 320x + x2 = 320 The x term is 320x. Take half its coefficient (160). Square it (25600) and add it to both sides. Add '25600' to each side of the equation. 320x + 25600 + x2 = 320 + 25600 Reorder the terms: 25600 + 320x + x2 = 320 + 25600 Combine like terms: 320 + 25600 = 25920 25600 + 320x + x2 = 25920 Factor a perfect square on the left side: (x + 160)(x + 160) = 25920 Calculate the square root of the right side: 160.99689438 Break this problem into two subproblems by setting (x + 160) equal to 160.99689438 and -160.99689438.Subproblem 1
x + 160 = 160.99689438 Simplifying x + 160 = 160.99689438 Reorder the terms: 160 + x = 160.99689438 Solving 160 + x = 160.99689438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-160' to each side of the equation. 160 + -160 + x = 160.99689438 + -160 Combine like terms: 160 + -160 = 0 0 + x = 160.99689438 + -160 x = 160.99689438 + -160 Combine like terms: 160.99689438 + -160 = 0.99689438 x = 0.99689438 Simplifying x = 0.99689438Subproblem 2
x + 160 = -160.99689438 Simplifying x + 160 = -160.99689438 Reorder the terms: 160 + x = -160.99689438 Solving 160 + x = -160.99689438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-160' to each side of the equation. 160 + -160 + x = -160.99689438 + -160 Combine like terms: 160 + -160 = 0 0 + x = -160.99689438 + -160 x = -160.99689438 + -160 Combine like terms: -160.99689438 + -160 = -320.99689438 x = -320.99689438 Simplifying x = -320.99689438Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.99689438, -320.99689438}
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