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Simplifying x2 + 6x + -1270 = 0 Reorder the terms: -1270 + 6x + x2 = 0 Solving -1270 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1270' to each side of the equation. -1270 + 6x + 1270 + x2 = 0 + 1270 Reorder the terms: -1270 + 1270 + 6x + x2 = 0 + 1270 Combine like terms: -1270 + 1270 = 0 0 + 6x + x2 = 0 + 1270 6x + x2 = 0 + 1270 Combine like terms: 0 + 1270 = 1270 6x + x2 = 1270 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 1270 + 9 Reorder the terms: 9 + 6x + x2 = 1270 + 9 Combine like terms: 1270 + 9 = 1279 9 + 6x + x2 = 1279 Factor a perfect square on the left side: (x + 3)(x + 3) = 1279 Calculate the square root of the right side: 35.763109484 Break this problem into two subproblems by setting (x + 3) equal to 35.763109484 and -35.763109484.Subproblem 1
x + 3 = 35.763109484 Simplifying x + 3 = 35.763109484 Reorder the terms: 3 + x = 35.763109484 Solving 3 + x = 35.763109484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 35.763109484 + -3 Combine like terms: 3 + -3 = 0 0 + x = 35.763109484 + -3 x = 35.763109484 + -3 Combine like terms: 35.763109484 + -3 = 32.763109484 x = 32.763109484 Simplifying x = 32.763109484Subproblem 2
x + 3 = -35.763109484 Simplifying x + 3 = -35.763109484 Reorder the terms: 3 + x = -35.763109484 Solving 3 + x = -35.763109484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -35.763109484 + -3 Combine like terms: 3 + -3 = 0 0 + x = -35.763109484 + -3 x = -35.763109484 + -3 Combine like terms: -35.763109484 + -3 = -38.763109484 x = -38.763109484 Simplifying x = -38.763109484Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.763109484, -38.763109484}
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