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Simplifying 7x + x2 + -208 = 0 Reorder the terms: -208 + 7x + x2 = 0 Solving -208 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '208' to each side of the equation. -208 + 7x + 208 + x2 = 0 + 208 Reorder the terms: -208 + 208 + 7x + x2 = 0 + 208 Combine like terms: -208 + 208 = 0 0 + 7x + x2 = 0 + 208 7x + x2 = 0 + 208 Combine like terms: 0 + 208 = 208 7x + x2 = 208 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 = 208 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 208 + 12.25 Combine like terms: 208 + 12.25 = 220.25 12.25 + 7x + x2 = 220.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 220.25 Calculate the square root of the right side: 14.84082208 Break this problem into two subproblems by setting (x + 3.5) equal to 14.84082208 and -14.84082208.Subproblem 1
x + 3.5 = 14.84082208 Simplifying x + 3.5 = 14.84082208 Reorder the terms: 3.5 + x = 14.84082208 Solving 3.5 + x = 14.84082208 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 = 14.84082208 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 14.84082208 + -3.5 x = 14.84082208 + -3.5 Combine like terms: 14.84082208 + -3.5 = 11.34082208 x = 11.34082208 Simplifying x = 11.34082208Subproblem 2
x + 3.5 = -14.84082208 Simplifying x + 3.5 = -14.84082208 Reorder the terms: 3.5 + x = -14.84082208 Solving 3.5 + x = -14.84082208 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 = -14.84082208 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -14.84082208 + -3.5 x = -14.84082208 + -3.5 Combine like terms: -14.84082208 + -3.5 = -18.34082208 x = -18.34082208 Simplifying x = -18.34082208Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.34082208, -18.34082208}
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