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Simplifying x2 + -98x + 100 = 0 Reorder the terms: 100 + -98x + x2 = 0 Solving 100 + -98x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -98x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -98x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -98x + x2 = 0 + -100 -98x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -98x + x2 = -100 The x term is -98x. Take half its coefficient (-49). Square it (2401) and add it to both sides. Add '2401' to each side of the equation. -98x + 2401 + x2 = -100 + 2401 Reorder the terms: 2401 + -98x + x2 = -100 + 2401 Combine like terms: -100 + 2401 = 2301 2401 + -98x + x2 = 2301 Factor a perfect square on the left side: (x + -49)(x + -49) = 2301 Calculate the square root of the right side: 47.968739821 Break this problem into two subproblems by setting (x + -49) equal to 47.968739821 and -47.968739821.Subproblem 1
x + -49 = 47.968739821 Simplifying x + -49 = 47.968739821 Reorder the terms: -49 + x = 47.968739821 Solving -49 + x = 47.968739821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + x = 47.968739821 + 49 Combine like terms: -49 + 49 = 0 0 + x = 47.968739821 + 49 x = 47.968739821 + 49 Combine like terms: 47.968739821 + 49 = 96.968739821 x = 96.968739821 Simplifying x = 96.968739821Subproblem 2
x + -49 = -47.968739821 Simplifying x + -49 = -47.968739821 Reorder the terms: -49 + x = -47.968739821 Solving -49 + x = -47.968739821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + x = -47.968739821 + 49 Combine like terms: -49 + 49 = 0 0 + x = -47.968739821 + 49 x = -47.968739821 + 49 Combine like terms: -47.968739821 + 49 = 1.031260179 x = 1.031260179 Simplifying x = 1.031260179Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.968739821, 1.031260179}
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