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Simplifying x2 + -647x + 196 = 0 Reorder the terms: 196 + -647x + x2 = 0 Solving 196 + -647x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-196' to each side of the equation. 196 + -647x + -196 + x2 = 0 + -196 Reorder the terms: 196 + -196 + -647x + x2 = 0 + -196 Combine like terms: 196 + -196 = 0 0 + -647x + x2 = 0 + -196 -647x + x2 = 0 + -196 Combine like terms: 0 + -196 = -196 -647x + x2 = -196 The x term is -647x. Take half its coefficient (-323.5). Square it (104652.25) and add it to both sides. Add '104652.25' to each side of the equation. -647x + 104652.25 + x2 = -196 + 104652.25 Reorder the terms: 104652.25 + -647x + x2 = -196 + 104652.25 Combine like terms: -196 + 104652.25 = 104456.25 104652.25 + -647x + x2 = 104456.25 Factor a perfect square on the left side: (x + -323.5)(x + -323.5) = 104456.25 Calculate the square root of the right side: 323.196921396 Break this problem into two subproblems by setting (x + -323.5) equal to 323.196921396 and -323.196921396.Subproblem 1
x + -323.5 = 323.196921396 Simplifying x + -323.5 = 323.196921396 Reorder the terms: -323.5 + x = 323.196921396 Solving -323.5 + x = 323.196921396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '323.5' to each side of the equation. -323.5 + 323.5 + x = 323.196921396 + 323.5 Combine like terms: -323.5 + 323.5 = 0.0 0.0 + x = 323.196921396 + 323.5 x = 323.196921396 + 323.5 Combine like terms: 323.196921396 + 323.5 = 646.696921396 x = 646.696921396 Simplifying x = 646.696921396Subproblem 2
x + -323.5 = -323.196921396 Simplifying x + -323.5 = -323.196921396 Reorder the terms: -323.5 + x = -323.196921396 Solving -323.5 + x = -323.196921396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '323.5' to each side of the equation. -323.5 + 323.5 + x = -323.196921396 + 323.5 Combine like terms: -323.5 + 323.5 = 0.0 0.0 + x = -323.196921396 + 323.5 x = -323.196921396 + 323.5 Combine like terms: -323.196921396 + 323.5 = 0.303078604 x = 0.303078604 Simplifying x = 0.303078604Solution
The solution to the problem is based on the solutions from the subproblems. x = {646.696921396, 0.303078604}
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