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Simplifying x2 + 4x + -474 = 0 Reorder the terms: -474 + 4x + x2 = 0 Solving -474 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '474' to each side of the equation. -474 + 4x + 474 + x2 = 0 + 474 Reorder the terms: -474 + 474 + 4x + x2 = 0 + 474 Combine like terms: -474 + 474 = 0 0 + 4x + x2 = 0 + 474 4x + x2 = 0 + 474 Combine like terms: 0 + 474 = 474 4x + x2 = 474 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 = 474 + 4 Reorder the terms: 4 + 4x + x2 = 474 + 4 Combine like terms: 474 + 4 = 478 4 + 4x + x2 = 478 Factor a perfect square on the left side: (x + 2)(x + 2) = 478 Calculate the square root of the right side: 21.863211109 Break this problem into two subproblems by setting (x + 2) equal to 21.863211109 and -21.863211109.Subproblem 1
x + 2 = 21.863211109 Simplifying x + 2 = 21.863211109 Reorder the terms: 2 + x = 21.863211109 Solving 2 + x = 21.863211109 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 = 21.863211109 + -2 Combine like terms: 2 + -2 = 0 0 + x = 21.863211109 + -2 x = 21.863211109 + -2 Combine like terms: 21.863211109 + -2 = 19.863211109 x = 19.863211109 Simplifying x = 19.863211109Subproblem 2
x + 2 = -21.863211109 Simplifying x + 2 = -21.863211109 Reorder the terms: 2 + x = -21.863211109 Solving 2 + x = -21.863211109 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 = -21.863211109 + -2 Combine like terms: 2 + -2 = 0 0 + x = -21.863211109 + -2 x = -21.863211109 + -2 Combine like terms: -21.863211109 + -2 = -23.863211109 x = -23.863211109 Simplifying x = -23.863211109Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.863211109, -23.863211109}
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