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Simplifying x2 + 7.666x + 13 = 0 Reorder the terms: 13 + 7.666x + x2 = 0 Solving 13 + 7.666x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 7.666x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 7.666x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 7.666x + x2 = 0 + -13 7.666x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 7.666x + x2 = -13 The x term is 7.666x. Take half its coefficient (3.833). Square it (14.691889) and add it to both sides. Add '14.691889' to each side of the equation. 7.666x + 14.691889 + x2 = -13 + 14.691889 Reorder the terms: 14.691889 + 7.666x + x2 = -13 + 14.691889 Combine like terms: -13 + 14.691889 = 1.691889 14.691889 + 7.666x + x2 = 1.691889 Factor a perfect square on the left side: (x + 3.833)(x + 3.833) = 1.691889 Calculate the square root of the right side: 1.300726336 Break this problem into two subproblems by setting (x + 3.833) equal to 1.300726336 and -1.300726336.Subproblem 1
x + 3.833 = 1.300726336 Simplifying x + 3.833 = 1.300726336 Reorder the terms: 3.833 + x = 1.300726336 Solving 3.833 + x = 1.300726336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833' to each side of the equation. 3.833 + -3.833 + x = 1.300726336 + -3.833 Combine like terms: 3.833 + -3.833 = 0.000 0.000 + x = 1.300726336 + -3.833 x = 1.300726336 + -3.833 Combine like terms: 1.300726336 + -3.833 = -2.532273664 x = -2.532273664 Simplifying x = -2.532273664Subproblem 2
x + 3.833 = -1.300726336 Simplifying x + 3.833 = -1.300726336 Reorder the terms: 3.833 + x = -1.300726336 Solving 3.833 + x = -1.300726336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833' to each side of the equation. 3.833 + -3.833 + x = -1.300726336 + -3.833 Combine like terms: 3.833 + -3.833 = 0.000 0.000 + x = -1.300726336 + -3.833 x = -1.300726336 + -3.833 Combine like terms: -1.300726336 + -3.833 = -5.133726336 x = -5.133726336 Simplifying x = -5.133726336Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.532273664, -5.133726336}
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