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Simplifying x2 + -7x + -249 = 0 Reorder the terms: -249 + -7x + x2 = 0 Solving -249 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '249' to each side of the equation. -249 + -7x + 249 + x2 = 0 + 249 Reorder the terms: -249 + 249 + -7x + x2 = 0 + 249 Combine like terms: -249 + 249 = 0 0 + -7x + x2 = 0 + 249 -7x + x2 = 0 + 249 Combine like terms: 0 + 249 = 249 -7x + x2 = 249 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 249 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 249 + 12.25 Combine like terms: 249 + 12.25 = 261.25 12.25 + -7x + x2 = 261.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 261.25 Calculate the square root of the right side: 16.163229875 Break this problem into two subproblems by setting (x + -3.5) equal to 16.163229875 and -16.163229875.Subproblem 1
x + -3.5 = 16.163229875 Simplifying x + -3.5 = 16.163229875 Reorder the terms: -3.5 + x = 16.163229875 Solving -3.5 + x = 16.163229875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 16.163229875 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 16.163229875 + 3.5 x = 16.163229875 + 3.5 Combine like terms: 16.163229875 + 3.5 = 19.663229875 x = 19.663229875 Simplifying x = 19.663229875Subproblem 2
x + -3.5 = -16.163229875 Simplifying x + -3.5 = -16.163229875 Reorder the terms: -3.5 + x = -16.163229875 Solving -3.5 + x = -16.163229875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -16.163229875 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -16.163229875 + 3.5 x = -16.163229875 + 3.5 Combine like terms: -16.163229875 + 3.5 = -12.663229875 x = -12.663229875 Simplifying x = -12.663229875Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.663229875, -12.663229875}
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