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Simplifying x2 + 2x + -1200 = 0 Reorder the terms: -1200 + 2x + x2 = 0 Solving -1200 + 2x + 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 + 2x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 2x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 2x + x2 = 0 + 1200 2x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 2x + x2 = 1200 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1200 + 1 Reorder the terms: 1 + 2x + x2 = 1200 + 1 Combine like terms: 1200 + 1 = 1201 1 + 2x + x2 = 1201 Factor a perfect square on the left side: (x + 1)(x + 1) = 1201 Calculate the square root of the right side: 34.655446902 Break this problem into two subproblems by setting (x + 1) equal to 34.655446902 and -34.655446902.Subproblem 1
x + 1 = 34.655446902 Simplifying x + 1 = 34.655446902 Reorder the terms: 1 + x = 34.655446902 Solving 1 + x = 34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 34.655446902 + -1 Combine like terms: 1 + -1 = 0 0 + x = 34.655446902 + -1 x = 34.655446902 + -1 Combine like terms: 34.655446902 + -1 = 33.655446902 x = 33.655446902 Simplifying x = 33.655446902Subproblem 2
x + 1 = -34.655446902 Simplifying x + 1 = -34.655446902 Reorder the terms: 1 + x = -34.655446902 Solving 1 + x = -34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -34.655446902 + -1 Combine like terms: 1 + -1 = 0 0 + x = -34.655446902 + -1 x = -34.655446902 + -1 Combine like terms: -34.655446902 + -1 = -35.655446902 x = -35.655446902 Simplifying x = -35.655446902Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.655446902, -35.655446902}
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