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Simplifying 320 = x(x + 2) Reorder the terms: 320 = x(2 + x) 320 = (2 * x + x * x) 320 = (2x + x2) Solving 320 = 2x + x2 Solving for variable 'x'. Reorder the terms: 320 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 320 + -2x + -1x2 = 0 + x2 + -1x2 320 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 320 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -320 + 2x + x2 = 0 Move the constant term to the right: Add '320' to each side of the equation. -320 + 2x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + 2x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 2x + x2 = 0 + 320 2x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 2x + x2 = 320 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 320 + 1 Reorder the terms: 1 + 2x + x2 = 320 + 1 Combine like terms: 320 + 1 = 321 1 + 2x + x2 = 321 Factor a perfect square on the left side: (x + 1)(x + 1) = 321 Calculate the square root of the right side: 17.916472867 Break this problem into two subproblems by setting (x + 1) equal to 17.916472867 and -17.916472867.Subproblem 1
x + 1 = 17.916472867 Simplifying x + 1 = 17.916472867 Reorder the terms: 1 + x = 17.916472867 Solving 1 + x = 17.916472867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 17.916472867 + -1 Combine like terms: 1 + -1 = 0 0 + x = 17.916472867 + -1 x = 17.916472867 + -1 Combine like terms: 17.916472867 + -1 = 16.916472867 x = 16.916472867 Simplifying x = 16.916472867Subproblem 2
x + 1 = -17.916472867 Simplifying x + 1 = -17.916472867 Reorder the terms: 1 + x = -17.916472867 Solving 1 + x = -17.916472867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -17.916472867 + -1 Combine like terms: 1 + -1 = 0 0 + x = -17.916472867 + -1 x = -17.916472867 + -1 Combine like terms: -17.916472867 + -1 = -18.916472867 x = -18.916472867 Simplifying x = -18.916472867Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.916472867, -18.916472867}
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