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Simplifying x2 + -8x + -98 = 0 Reorder the terms: -98 + -8x + x2 = 0 Solving -98 + -8x + 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 + -8x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -8x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -8x + x2 = 0 + 98 -8x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -8x + x2 = 98 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 98 + 16 Reorder the terms: 16 + -8x + x2 = 98 + 16 Combine like terms: 98 + 16 = 114 16 + -8x + x2 = 114 Factor a perfect square on the left side: (x + -4)(x + -4) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + -4) equal to 10.677078252 and -10.677078252.Subproblem 1
x + -4 = 10.677078252 Simplifying x + -4 = 10.677078252 Reorder the terms: -4 + x = 10.677078252 Solving -4 + x = 10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 10.677078252 + 4 Combine like terms: -4 + 4 = 0 0 + x = 10.677078252 + 4 x = 10.677078252 + 4 Combine like terms: 10.677078252 + 4 = 14.677078252 x = 14.677078252 Simplifying x = 14.677078252Subproblem 2
x + -4 = -10.677078252 Simplifying x + -4 = -10.677078252 Reorder the terms: -4 + x = -10.677078252 Solving -4 + x = -10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -10.677078252 + 4 Combine like terms: -4 + 4 = 0 0 + x = -10.677078252 + 4 x = -10.677078252 + 4 Combine like terms: -10.677078252 + 4 = -6.677078252 x = -6.677078252 Simplifying x = -6.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.677078252, -6.677078252}
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