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Simplifying x2 + -2x + -420 = 0 Reorder the terms: -420 + -2x + x2 = 0 Solving -420 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '420' to each side of the equation. -420 + -2x + 420 + x2 = 0 + 420 Reorder the terms: -420 + 420 + -2x + x2 = 0 + 420 Combine like terms: -420 + 420 = 0 0 + -2x + x2 = 0 + 420 -2x + x2 = 0 + 420 Combine like terms: 0 + 420 = 420 -2x + x2 = 420 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 = 420 + 1 Reorder the terms: 1 + -2x + x2 = 420 + 1 Combine like terms: 420 + 1 = 421 1 + -2x + x2 = 421 Factor a perfect square on the left side: (x + -1)(x + -1) = 421 Calculate the square root of the right side: 20.518284529 Break this problem into two subproblems by setting (x + -1) equal to 20.518284529 and -20.518284529.Subproblem 1
x + -1 = 20.518284529 Simplifying x + -1 = 20.518284529 Reorder the terms: -1 + x = 20.518284529 Solving -1 + x = 20.518284529 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 = 20.518284529 + 1 Combine like terms: -1 + 1 = 0 0 + x = 20.518284529 + 1 x = 20.518284529 + 1 Combine like terms: 20.518284529 + 1 = 21.518284529 x = 21.518284529 Simplifying x = 21.518284529Subproblem 2
x + -1 = -20.518284529 Simplifying x + -1 = -20.518284529 Reorder the terms: -1 + x = -20.518284529 Solving -1 + x = -20.518284529 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 = -20.518284529 + 1 Combine like terms: -1 + 1 = 0 0 + x = -20.518284529 + 1 x = -20.518284529 + 1 Combine like terms: -20.518284529 + 1 = -19.518284529 x = -19.518284529 Simplifying x = -19.518284529Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.518284529, -19.518284529}
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