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Simplifying x2 + 2x + -432 = 0 Reorder the terms: -432 + 2x + x2 = 0 Solving -432 + 2x + x2 = 0 Solving for variable 'x'. 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 = 19.808652047 x = 19.808652047 Simplifying x = 19.808652047Subproblem 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 = -21.808652047 x = -21.808652047 Simplifying x = -21.808652047Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.808652047, -21.808652047}
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