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Simplifying x(x + -2) = 432 Reorder the terms: x(-2 + x) = 432 (-2 * x + x * x) = 432 (-2x + x2) = 432 Solving -2x + x2 = 432 Solving for variable 'x'. Reorder the terms: -432 + -2x + x2 = 432 + -432 Combine like terms: 432 + -432 = 0 -432 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '432' to each side of the equation. -432 + -2x + 432 + x2 = 0 + 432 Reorder the terms: -432 + 432 + -2x + x2 = 0 + 432 Combine like terms: -432 + 432 = 0 0 + -2x + x2 = 0 + 432 -2x + x2 = 0 + 432 Combine like terms: 0 + 432 = 432 -2x + x2 = 432 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 = 432 + 1 Reorder the terms: 1 + -2x + x2 = 432 + 1 Combine like terms: 432 + 1 = 433 1 + -2x + x2 = 433 Factor a perfect square on the left side: (x + -1)(x + -1) = 433 Calculate the square root of the right side: 20.808652047 Break this problem into two subproblems by setting (x + -1) equal to 20.808652047 and -20.808652047.Subproblem 1
x + -1 = 20.808652047 Simplifying x + -1 = 20.808652047 Reorder the terms: -1 + x = 20.808652047 Solving -1 + x = 20.808652047 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 = 20.808652047 + 1 Combine like terms: -1 + 1 = 0 0 + x = 20.808652047 + 1 x = 20.808652047 + 1 Combine like terms: 20.808652047 + 1 = 21.808652047 x = 21.808652047 Simplifying x = 21.808652047Subproblem 2
x + -1 = -20.808652047 Simplifying x + -1 = -20.808652047 Reorder the terms: -1 + x = -20.808652047 Solving -1 + x = -20.808652047 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 = -20.808652047 + 1 Combine like terms: -1 + 1 = 0 0 + x = -20.808652047 + 1 x = -20.808652047 + 1 Combine like terms: -20.808652047 + 1 = -19.808652047 x = -19.808652047 Simplifying x = -19.808652047Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.808652047, -19.808652047}
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