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Simplifying x2 + 7x + 8 = 392 Reorder the terms: 8 + 7x + x2 = 392 Solving 8 + 7x + x2 = 392 Solving for variable 'x'. Reorder the terms: 8 + -392 + 7x + x2 = 392 + -392 Combine like terms: 8 + -392 = -384 -384 + 7x + x2 = 392 + -392 Combine like terms: 392 + -392 = 0 -384 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '384' to each side of the equation. -384 + 7x + 384 + x2 = 0 + 384 Reorder the terms: -384 + 384 + 7x + x2 = 0 + 384 Combine like terms: -384 + 384 = 0 0 + 7x + x2 = 0 + 384 7x + x2 = 0 + 384 Combine like terms: 0 + 384 = 384 7x + x2 = 384 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 = 384 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 384 + 12.25 Combine like terms: 384 + 12.25 = 396.25 12.25 + 7x + x2 = 396.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 396.25 Calculate the square root of the right side: 19.906029237 Break this problem into two subproblems by setting (x + 3.5) equal to 19.906029237 and -19.906029237.Subproblem 1
x + 3.5 = 19.906029237 Simplifying x + 3.5 = 19.906029237 Reorder the terms: 3.5 + x = 19.906029237 Solving 3.5 + x = 19.906029237 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 = 19.906029237 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 19.906029237 + -3.5 x = 19.906029237 + -3.5 Combine like terms: 19.906029237 + -3.5 = 16.406029237 x = 16.406029237 Simplifying x = 16.406029237Subproblem 2
x + 3.5 = -19.906029237 Simplifying x + 3.5 = -19.906029237 Reorder the terms: 3.5 + x = -19.906029237 Solving 3.5 + x = -19.906029237 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 = -19.906029237 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -19.906029237 + -3.5 x = -19.906029237 + -3.5 Combine like terms: -19.906029237 + -3.5 = -23.406029237 x = -23.406029237 Simplifying x = -23.406029237Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.406029237, -23.406029237}
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