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Simplifying x2 + 6x + -860 = 0 Reorder the terms: -860 + 6x + x2 = 0 Solving -860 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '860' to each side of the equation. -860 + 6x + 860 + x2 = 0 + 860 Reorder the terms: -860 + 860 + 6x + x2 = 0 + 860 Combine like terms: -860 + 860 = 0 0 + 6x + x2 = 0 + 860 6x + x2 = 0 + 860 Combine like terms: 0 + 860 = 860 6x + x2 = 860 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 = 860 + 9 Reorder the terms: 9 + 6x + x2 = 860 + 9 Combine like terms: 860 + 9 = 869 9 + 6x + x2 = 869 Factor a perfect square on the left side: (x + 3)(x + 3) = 869 Calculate the square root of the right side: 29.478805946 Break this problem into two subproblems by setting (x + 3) equal to 29.478805946 and -29.478805946.Subproblem 1
x + 3 = 29.478805946 Simplifying x + 3 = 29.478805946 Reorder the terms: 3 + x = 29.478805946 Solving 3 + x = 29.478805946 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 = 29.478805946 + -3 Combine like terms: 3 + -3 = 0 0 + x = 29.478805946 + -3 x = 29.478805946 + -3 Combine like terms: 29.478805946 + -3 = 26.478805946 x = 26.478805946 Simplifying x = 26.478805946Subproblem 2
x + 3 = -29.478805946 Simplifying x + 3 = -29.478805946 Reorder the terms: 3 + x = -29.478805946 Solving 3 + x = -29.478805946 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 = -29.478805946 + -3 Combine like terms: 3 + -3 = 0 0 + x = -29.478805946 + -3 x = -29.478805946 + -3 Combine like terms: -29.478805946 + -3 = -32.478805946 x = -32.478805946 Simplifying x = -32.478805946Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.478805946, -32.478805946}
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