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Simplifying x2 + -84x + 100 = 0 Reorder the terms: 100 + -84x + x2 = 0 Solving 100 + -84x + 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 + -84x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -84x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -84x + x2 = 0 + -100 -84x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -84x + x2 = -100 The x term is -84x. Take half its coefficient (-42). Square it (1764) and add it to both sides. Add '1764' to each side of the equation. -84x + 1764 + x2 = -100 + 1764 Reorder the terms: 1764 + -84x + x2 = -100 + 1764 Combine like terms: -100 + 1764 = 1664 1764 + -84x + x2 = 1664 Factor a perfect square on the left side: (x + -42)(x + -42) = 1664 Calculate the square root of the right side: 40.792156109 Break this problem into two subproblems by setting (x + -42) equal to 40.792156109 and -40.792156109.Subproblem 1
x + -42 = 40.792156109 Simplifying x + -42 = 40.792156109 Reorder the terms: -42 + x = 40.792156109 Solving -42 + x = 40.792156109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = 40.792156109 + 42 Combine like terms: -42 + 42 = 0 0 + x = 40.792156109 + 42 x = 40.792156109 + 42 Combine like terms: 40.792156109 + 42 = 82.792156109 x = 82.792156109 Simplifying x = 82.792156109Subproblem 2
x + -42 = -40.792156109 Simplifying x + -42 = -40.792156109 Reorder the terms: -42 + x = -40.792156109 Solving -42 + x = -40.792156109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = -40.792156109 + 42 Combine like terms: -42 + 42 = 0 0 + x = -40.792156109 + 42 x = -40.792156109 + 42 Combine like terms: -40.792156109 + 42 = 1.207843891 x = 1.207843891 Simplifying x = 1.207843891Solution
The solution to the problem is based on the solutions from the subproblems. x = {82.792156109, 1.207843891}
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