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Simplifying x2 + 6x + -107 = 0 Reorder the terms: -107 + 6x + x2 = 0 Solving -107 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '107' to each side of the equation. -107 + 6x + 107 + x2 = 0 + 107 Reorder the terms: -107 + 107 + 6x + x2 = 0 + 107 Combine like terms: -107 + 107 = 0 0 + 6x + x2 = 0 + 107 6x + x2 = 0 + 107 Combine like terms: 0 + 107 = 107 6x + x2 = 107 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 = 107 + 9 Reorder the terms: 9 + 6x + x2 = 107 + 9 Combine like terms: 107 + 9 = 116 9 + 6x + x2 = 116 Factor a perfect square on the left side: (x + 3)(x + 3) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + 3) equal to 10.770329614 and -10.770329614.Subproblem 1
x + 3 = 10.770329614 Simplifying x + 3 = 10.770329614 Reorder the terms: 3 + x = 10.770329614 Solving 3 + x = 10.770329614 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 = 10.770329614 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.770329614 + -3 x = 10.770329614 + -3 Combine like terms: 10.770329614 + -3 = 7.770329614 x = 7.770329614 Simplifying x = 7.770329614Subproblem 2
x + 3 = -10.770329614 Simplifying x + 3 = -10.770329614 Reorder the terms: 3 + x = -10.770329614 Solving 3 + x = -10.770329614 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 = -10.770329614 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.770329614 + -3 x = -10.770329614 + -3 Combine like terms: -10.770329614 + -3 = -13.770329614 x = -13.770329614 Simplifying x = -13.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.770329614, -13.770329614}
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