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Simplifying x2 + -12x + -98 = 0 Reorder the terms: -98 + -12x + x2 = 0 Solving -98 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -12x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -12x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -12x + x2 = 0 + 98 -12x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -12x + x2 = 98 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 98 + 36 Reorder the terms: 36 + -12x + x2 = 98 + 36 Combine like terms: 98 + 36 = 134 36 + -12x + x2 = 134 Factor a perfect square on the left side: (x + -6)(x + -6) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (x + -6) equal to 11.575836903 and -11.575836903.Subproblem 1
x + -6 = 11.575836903 Simplifying x + -6 = 11.575836903 Reorder the terms: -6 + x = 11.575836903 Solving -6 + x = 11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 11.575836903 + 6 Combine like terms: -6 + 6 = 0 0 + x = 11.575836903 + 6 x = 11.575836903 + 6 Combine like terms: 11.575836903 + 6 = 17.575836903 x = 17.575836903 Simplifying x = 17.575836903Subproblem 2
x + -6 = -11.575836903 Simplifying x + -6 = -11.575836903 Reorder the terms: -6 + x = -11.575836903 Solving -6 + x = -11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -11.575836903 + 6 Combine like terms: -6 + 6 = 0 0 + x = -11.575836903 + 6 x = -11.575836903 + 6 Combine like terms: -11.575836903 + 6 = -5.575836903 x = -5.575836903 Simplifying x = -5.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.575836903, -5.575836903}
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