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Simplifying x2 + 7x = 400 Reorder the terms: 7x + x2 = 400 Solving 7x + x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 7x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 7x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 7x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 7x + x2 = 0 + 400 7x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 7x + x2 = 400 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 = 400 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 400 + 12.25 Combine like terms: 400 + 12.25 = 412.25 12.25 + 7x + x2 = 412.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 412.25 Calculate the square root of the right side: 20.303940504 Break this problem into two subproblems by setting (x + 3.5) equal to 20.303940504 and -20.303940504.Subproblem 1
x + 3.5 = 20.303940504 Simplifying x + 3.5 = 20.303940504 Reorder the terms: 3.5 + x = 20.303940504 Solving 3.5 + x = 20.303940504 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 = 20.303940504 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 20.303940504 + -3.5 x = 20.303940504 + -3.5 Combine like terms: 20.303940504 + -3.5 = 16.803940504 x = 16.803940504 Simplifying x = 16.803940504Subproblem 2
x + 3.5 = -20.303940504 Simplifying x + 3.5 = -20.303940504 Reorder the terms: 3.5 + x = -20.303940504 Solving 3.5 + x = -20.303940504 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 = -20.303940504 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -20.303940504 + -3.5 x = -20.303940504 + -3.5 Combine like terms: -20.303940504 + -3.5 = -23.803940504 x = -23.803940504 Simplifying x = -23.803940504Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.803940504, -23.803940504}
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