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Simplifying x2 + 7x + -392 = 0 Reorder the terms: -392 + 7x + x2 = 0 Solving -392 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '392' to each side of the equation. -392 + 7x + 392 + x2 = 0 + 392 Reorder the terms: -392 + 392 + 7x + x2 = 0 + 392 Combine like terms: -392 + 392 = 0 0 + 7x + x2 = 0 + 392 7x + x2 = 0 + 392 Combine like terms: 0 + 392 = 392 7x + x2 = 392 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 = 392 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 392 + 12.25 Combine like terms: 392 + 12.25 = 404.25 12.25 + 7x + x2 = 404.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 404.25 Calculate the square root of the right side: 20.105969263 Break this problem into two subproblems by setting (x + 3.5) equal to 20.105969263 and -20.105969263.Subproblem 1
x + 3.5 = 20.105969263 Simplifying x + 3.5 = 20.105969263 Reorder the terms: 3.5 + x = 20.105969263 Solving 3.5 + x = 20.105969263 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 = 20.105969263 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 20.105969263 + -3.5 x = 20.105969263 + -3.5 Combine like terms: 20.105969263 + -3.5 = 16.605969263 x = 16.605969263 Simplifying x = 16.605969263Subproblem 2
x + 3.5 = -20.105969263 Simplifying x + 3.5 = -20.105969263 Reorder the terms: 3.5 + x = -20.105969263 Solving 3.5 + x = -20.105969263 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 = -20.105969263 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -20.105969263 + -3.5 x = -20.105969263 + -3.5 Combine like terms: -20.105969263 + -3.5 = -23.605969263 x = -23.605969263 Simplifying x = -23.605969263Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.605969263, -23.605969263}
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