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Simplifying x * x + 4x + -8400 = 0 Multiply x * x x2 + 4x + -8400 = 0 Reorder the terms: -8400 + 4x + x2 = 0 Solving -8400 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8400' to each side of the equation. -8400 + 4x + 8400 + x2 = 0 + 8400 Reorder the terms: -8400 + 8400 + 4x + x2 = 0 + 8400 Combine like terms: -8400 + 8400 = 0 0 + 4x + x2 = 0 + 8400 4x + x2 = 0 + 8400 Combine like terms: 0 + 8400 = 8400 4x + x2 = 8400 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 = 8400 + 4 Reorder the terms: 4 + 4x + x2 = 8400 + 4 Combine like terms: 8400 + 4 = 8404 4 + 4x + x2 = 8404 Factor a perfect square on the left side: (x + 2)(x + 2) = 8404 Calculate the square root of the right side: 91.673333091 Break this problem into two subproblems by setting (x + 2) equal to 91.673333091 and -91.673333091.Subproblem 1
x + 2 = 91.673333091 Simplifying x + 2 = 91.673333091 Reorder the terms: 2 + x = 91.673333091 Solving 2 + x = 91.673333091 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 = 91.673333091 + -2 Combine like terms: 2 + -2 = 0 0 + x = 91.673333091 + -2 x = 91.673333091 + -2 Combine like terms: 91.673333091 + -2 = 89.673333091 x = 89.673333091 Simplifying x = 89.673333091Subproblem 2
x + 2 = -91.673333091 Simplifying x + 2 = -91.673333091 Reorder the terms: 2 + x = -91.673333091 Solving 2 + x = -91.673333091 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 = -91.673333091 + -2 Combine like terms: 2 + -2 = 0 0 + x = -91.673333091 + -2 x = -91.673333091 + -2 Combine like terms: -91.673333091 + -2 = -93.673333091 x = -93.673333091 Simplifying x = -93.673333091Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.673333091, -93.673333091}
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