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Simplifying x2 + -2x + -98 = 0 Reorder the terms: -98 + -2x + x2 = 0 Solving -98 + -2x + 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 + -2x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -2x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -2x + x2 = 0 + 98 -2x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -2x + x2 = 98 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 98 + 1 Reorder the terms: 1 + -2x + x2 = 98 + 1 Combine like terms: 98 + 1 = 99 1 + -2x + x2 = 99 Factor a perfect square on the left side: (x + -1)(x + -1) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + -1) equal to 9.949874371 and -9.949874371.Subproblem 1
x + -1 = 9.949874371 Simplifying x + -1 = 9.949874371 Reorder the terms: -1 + x = 9.949874371 Solving -1 + x = 9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.949874371 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.949874371 + 1 x = 9.949874371 + 1 Combine like terms: 9.949874371 + 1 = 10.949874371 x = 10.949874371 Simplifying x = 10.949874371Subproblem 2
x + -1 = -9.949874371 Simplifying x + -1 = -9.949874371 Reorder the terms: -1 + x = -9.949874371 Solving -1 + x = -9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.949874371 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.949874371 + 1 x = -9.949874371 + 1 Combine like terms: -9.949874371 + 1 = -8.949874371 x = -8.949874371 Simplifying x = -8.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.949874371, -8.949874371}
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