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Simplifying 5x + x2 = 168 Solving 5x + x2 = 168 Solving for variable 'x'. Reorder the terms: -168 + 5x + x2 = 168 + -168 Combine like terms: 168 + -168 = 0 -168 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + 5x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + 5x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + 5x + x2 = 0 + 168 5x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 5x + x2 = 168 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 168 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 168 + 6.25 Combine like terms: 168 + 6.25 = 174.25 6.25 + 5x + x2 = 174.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + 2.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + 2.5 = 13.200378782 Simplifying x + 2.5 = 13.200378782 Reorder the terms: 2.5 + x = 13.200378782 Solving 2.5 + x = 13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 13.200378782 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.200378782 + -2.5 x = 13.200378782 + -2.5 Combine like terms: 13.200378782 + -2.5 = 10.700378782 x = 10.700378782 Simplifying x = 10.700378782Subproblem 2
x + 2.5 = -13.200378782 Simplifying x + 2.5 = -13.200378782 Reorder the terms: 2.5 + x = -13.200378782 Solving 2.5 + x = -13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -13.200378782 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.200378782 + -2.5 x = -13.200378782 + -2.5 Combine like terms: -13.200378782 + -2.5 = -15.700378782 x = -15.700378782 Simplifying x = -15.700378782Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.700378782, -15.700378782}
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