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Simplifying x2 + 4x + -441 = 0 Reorder the terms: -441 + 4x + x2 = 0 Solving -441 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '441' to each side of the equation. -441 + 4x + 441 + x2 = 0 + 441 Reorder the terms: -441 + 441 + 4x + x2 = 0 + 441 Combine like terms: -441 + 441 = 0 0 + 4x + x2 = 0 + 441 4x + x2 = 0 + 441 Combine like terms: 0 + 441 = 441 4x + x2 = 441 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 = 441 + 4 Reorder the terms: 4 + 4x + x2 = 441 + 4 Combine like terms: 441 + 4 = 445 4 + 4x + x2 = 445 Factor a perfect square on the left side: (x + 2)(x + 2) = 445 Calculate the square root of the right side: 21.09502311 Break this problem into two subproblems by setting (x + 2) equal to 21.09502311 and -21.09502311.Subproblem 1
x + 2 = 21.09502311 Simplifying x + 2 = 21.09502311 Reorder the terms: 2 + x = 21.09502311 Solving 2 + x = 21.09502311 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 = 21.09502311 + -2 Combine like terms: 2 + -2 = 0 0 + x = 21.09502311 + -2 x = 21.09502311 + -2 Combine like terms: 21.09502311 + -2 = 19.09502311 x = 19.09502311 Simplifying x = 19.09502311Subproblem 2
x + 2 = -21.09502311 Simplifying x + 2 = -21.09502311 Reorder the terms: 2 + x = -21.09502311 Solving 2 + x = -21.09502311 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 = -21.09502311 + -2 Combine like terms: 2 + -2 = 0 0 + x = -21.09502311 + -2 x = -21.09502311 + -2 Combine like terms: -21.09502311 + -2 = -23.09502311 x = -23.09502311 Simplifying x = -23.09502311Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.09502311, -23.09502311}
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