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Simplifying 13x + x2 = 75 Solving 13x + x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 13x + x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 13x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 13x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 13x + x2 = 0 + 75 13x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 13x + x2 = 75 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 75 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 75 + 42.25 Combine like terms: 75 + 42.25 = 117.25 42.25 + 13x + x2 = 117.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 117.25 Calculate the square root of the right side: 10.828203914 Break this problem into two subproblems by setting (x + 6.5) equal to 10.828203914 and -10.828203914.Subproblem 1
x + 6.5 = 10.828203914 Simplifying x + 6.5 = 10.828203914 Reorder the terms: 6.5 + x = 10.828203914 Solving 6.5 + x = 10.828203914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 10.828203914 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 10.828203914 + -6.5 x = 10.828203914 + -6.5 Combine like terms: 10.828203914 + -6.5 = 4.328203914 x = 4.328203914 Simplifying x = 4.328203914Subproblem 2
x + 6.5 = -10.828203914 Simplifying x + 6.5 = -10.828203914 Reorder the terms: 6.5 + x = -10.828203914 Solving 6.5 + x = -10.828203914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -10.828203914 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -10.828203914 + -6.5 x = -10.828203914 + -6.5 Combine like terms: -10.828203914 + -6.5 = -17.328203914 x = -17.328203914 Simplifying x = -17.328203914Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.328203914, -17.328203914}
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