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Simplifying x2 + -4x + -471 = 0 Reorder the terms: -471 + -4x + x2 = 0 Solving -471 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '471' to each side of the equation. -471 + -4x + 471 + x2 = 0 + 471 Reorder the terms: -471 + 471 + -4x + x2 = 0 + 471 Combine like terms: -471 + 471 = 0 0 + -4x + x2 = 0 + 471 -4x + x2 = 0 + 471 Combine like terms: 0 + 471 = 471 -4x + x2 = 471 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 471 + 4 Reorder the terms: 4 + -4x + x2 = 471 + 4 Combine like terms: 471 + 4 = 475 4 + -4x + x2 = 475 Factor a perfect square on the left side: (x + -2)(x + -2) = 475 Calculate the square root of the right side: 21.794494718 Break this problem into two subproblems by setting (x + -2) equal to 21.794494718 and -21.794494718.Subproblem 1
x + -2 = 21.794494718 Simplifying x + -2 = 21.794494718 Reorder the terms: -2 + x = 21.794494718 Solving -2 + x = 21.794494718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 21.794494718 + 2 Combine like terms: -2 + 2 = 0 0 + x = 21.794494718 + 2 x = 21.794494718 + 2 Combine like terms: 21.794494718 + 2 = 23.794494718 x = 23.794494718 Simplifying x = 23.794494718Subproblem 2
x + -2 = -21.794494718 Simplifying x + -2 = -21.794494718 Reorder the terms: -2 + x = -21.794494718 Solving -2 + x = -21.794494718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -21.794494718 + 2 Combine like terms: -2 + 2 = 0 0 + x = -21.794494718 + 2 x = -21.794494718 + 2 Combine like terms: -21.794494718 + 2 = -19.794494718 x = -19.794494718 Simplifying x = -19.794494718Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.794494718, -19.794494718}
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