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Simplifying x2 + 4x + -1140 = 0 Reorder the terms: -1140 + 4x + x2 = 0 Solving -1140 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1140' to each side of the equation. -1140 + 4x + 1140 + x2 = 0 + 1140 Reorder the terms: -1140 + 1140 + 4x + x2 = 0 + 1140 Combine like terms: -1140 + 1140 = 0 0 + 4x + x2 = 0 + 1140 4x + x2 = 0 + 1140 Combine like terms: 0 + 1140 = 1140 4x + x2 = 1140 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 = 1140 + 4 Reorder the terms: 4 + 4x + x2 = 1140 + 4 Combine like terms: 1140 + 4 = 1144 4 + 4x + x2 = 1144 Factor a perfect square on the left side: (x + 2)(x + 2) = 1144 Calculate the square root of the right side: 33.823069051 Break this problem into two subproblems by setting (x + 2) equal to 33.823069051 and -33.823069051.Subproblem 1
x + 2 = 33.823069051 Simplifying x + 2 = 33.823069051 Reorder the terms: 2 + x = 33.823069051 Solving 2 + x = 33.823069051 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 = 33.823069051 + -2 Combine like terms: 2 + -2 = 0 0 + x = 33.823069051 + -2 x = 33.823069051 + -2 Combine like terms: 33.823069051 + -2 = 31.823069051 x = 31.823069051 Simplifying x = 31.823069051Subproblem 2
x + 2 = -33.823069051 Simplifying x + 2 = -33.823069051 Reorder the terms: 2 + x = -33.823069051 Solving 2 + x = -33.823069051 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 = -33.823069051 + -2 Combine like terms: 2 + -2 = 0 0 + x = -33.823069051 + -2 x = -33.823069051 + -2 Combine like terms: -33.823069051 + -2 = -35.823069051 x = -35.823069051 Simplifying x = -35.823069051Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.823069051, -35.823069051}
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