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Simplifying x2 + 4x + -1200 = 0 Reorder the terms: -1200 + 4x + x2 = 0 Solving -1200 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 4x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 4x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 4x + x2 = 0 + 1200 4x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 4x + x2 = 1200 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 = 1200 + 4 Reorder the terms: 4 + 4x + x2 = 1200 + 4 Combine like terms: 1200 + 4 = 1204 4 + 4x + x2 = 1204 Factor a perfect square on the left side: (x + 2)(x + 2) = 1204 Calculate the square root of the right side: 34.698703146 Break this problem into two subproblems by setting (x + 2) equal to 34.698703146 and -34.698703146.Subproblem 1
x + 2 = 34.698703146 Simplifying x + 2 = 34.698703146 Reorder the terms: 2 + x = 34.698703146 Solving 2 + x = 34.698703146 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 = 34.698703146 + -2 Combine like terms: 2 + -2 = 0 0 + x = 34.698703146 + -2 x = 34.698703146 + -2 Combine like terms: 34.698703146 + -2 = 32.698703146 x = 32.698703146 Simplifying x = 32.698703146Subproblem 2
x + 2 = -34.698703146 Simplifying x + 2 = -34.698703146 Reorder the terms: 2 + x = -34.698703146 Solving 2 + x = -34.698703146 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 = -34.698703146 + -2 Combine like terms: 2 + -2 = 0 0 + x = -34.698703146 + -2 x = -34.698703146 + -2 Combine like terms: -34.698703146 + -2 = -36.698703146 x = -36.698703146 Simplifying x = -36.698703146Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.698703146, -36.698703146}
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