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Simplifying x2 + 7x = 105 Reorder the terms: 7x + x2 = 105 Solving 7x + x2 = 105 Solving for variable 'x'. Reorder the terms: -105 + 7x + x2 = 105 + -105 Combine like terms: 105 + -105 = 0 -105 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + 7x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 7x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 7x + x2 = 0 + 105 7x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 7x + x2 = 105 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 = 105 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 105 + 12.25 Combine like terms: 105 + 12.25 = 117.25 12.25 + 7x + x2 = 117.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 117.25 Calculate the square root of the right side: 10.828203914 Break this problem into two subproblems by setting (x + 3.5) equal to 10.828203914 and -10.828203914.Subproblem 1
x + 3.5 = 10.828203914 Simplifying x + 3.5 = 10.828203914 Reorder the terms: 3.5 + x = 10.828203914 Solving 3.5 + x = 10.828203914 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 = 10.828203914 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 10.828203914 + -3.5 x = 10.828203914 + -3.5 Combine like terms: 10.828203914 + -3.5 = 7.328203914 x = 7.328203914 Simplifying x = 7.328203914Subproblem 2
x + 3.5 = -10.828203914 Simplifying x + 3.5 = -10.828203914 Reorder the terms: 3.5 + x = -10.828203914 Solving 3.5 + x = -10.828203914 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 = -10.828203914 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -10.828203914 + -3.5 x = -10.828203914 + -3.5 Combine like terms: -10.828203914 + -3.5 = -14.328203914 x = -14.328203914 Simplifying x = -14.328203914Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.328203914, -14.328203914}
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