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Simplifying x2 + 28x + -104 = 0 Reorder the terms: -104 + 28x + x2 = 0 Solving -104 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + 28x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + 28x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 28x + x2 = 0 + 104 28x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 28x + x2 = 104 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 104 + 196 Reorder the terms: 196 + 28x + x2 = 104 + 196 Combine like terms: 104 + 196 = 300 196 + 28x + x2 = 300 Factor a perfect square on the left side: (x + 14)(x + 14) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (x + 14) equal to 17.320508076 and -17.320508076.Subproblem 1
x + 14 = 17.320508076 Simplifying x + 14 = 17.320508076 Reorder the terms: 14 + x = 17.320508076 Solving 14 + x = 17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 17.320508076 + -14 Combine like terms: 14 + -14 = 0 0 + x = 17.320508076 + -14 x = 17.320508076 + -14 Combine like terms: 17.320508076 + -14 = 3.320508076 x = 3.320508076 Simplifying x = 3.320508076Subproblem 2
x + 14 = -17.320508076 Simplifying x + 14 = -17.320508076 Reorder the terms: 14 + x = -17.320508076 Solving 14 + x = -17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -17.320508076 + -14 Combine like terms: 14 + -14 = 0 0 + x = -17.320508076 + -14 x = -17.320508076 + -14 Combine like terms: -17.320508076 + -14 = -31.320508076 x = -31.320508076 Simplifying x = -31.320508076Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.320508076, -31.320508076}
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