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Simplifying x2 + 7x = 256 Reorder the terms: 7x + x2 = 256 Solving 7x + x2 = 256 Solving for variable 'x'. Reorder the terms: -256 + 7x + x2 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + 7x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 7x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 7x + x2 = 0 + 256 7x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 7x + x2 = 256 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 = 256 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 256 + 12.25 Combine like terms: 256 + 12.25 = 268.25 12.25 + 7x + x2 = 268.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 268.25 Calculate the square root of the right side: 16.378339354 Break this problem into two subproblems by setting (x + 3.5) equal to 16.378339354 and -16.378339354.Subproblem 1
x + 3.5 = 16.378339354 Simplifying x + 3.5 = 16.378339354 Reorder the terms: 3.5 + x = 16.378339354 Solving 3.5 + x = 16.378339354 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 = 16.378339354 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 16.378339354 + -3.5 x = 16.378339354 + -3.5 Combine like terms: 16.378339354 + -3.5 = 12.878339354 x = 12.878339354 Simplifying x = 12.878339354Subproblem 2
x + 3.5 = -16.378339354 Simplifying x + 3.5 = -16.378339354 Reorder the terms: 3.5 + x = -16.378339354 Solving 3.5 + x = -16.378339354 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 = -16.378339354 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -16.378339354 + -3.5 x = -16.378339354 + -3.5 Combine like terms: -16.378339354 + -3.5 = -19.878339354 x = -19.878339354 Simplifying x = -19.878339354Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.878339354, -19.878339354}
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