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Simplifying x2 + 5x = 432 Reorder the terms: 5x + x2 = 432 Solving 5x + x2 = 432 Solving for variable 'x'. Reorder the terms: -432 + 5x + x2 = 432 + -432 Combine like terms: 432 + -432 = 0 -432 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '432' to each side of the equation. -432 + 5x + 432 + x2 = 0 + 432 Reorder the terms: -432 + 432 + 5x + x2 = 0 + 432 Combine like terms: -432 + 432 = 0 0 + 5x + x2 = 0 + 432 5x + x2 = 0 + 432 Combine like terms: 0 + 432 = 432 5x + x2 = 432 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 = 432 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 432 + 6.25 Combine like terms: 432 + 6.25 = 438.25 6.25 + 5x + x2 = 438.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 438.25 Calculate the square root of the right side: 20.934421415 Break this problem into two subproblems by setting (x + 2.5) equal to 20.934421415 and -20.934421415.Subproblem 1
x + 2.5 = 20.934421415 Simplifying x + 2.5 = 20.934421415 Reorder the terms: 2.5 + x = 20.934421415 Solving 2.5 + x = 20.934421415 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 = 20.934421415 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 20.934421415 + -2.5 x = 20.934421415 + -2.5 Combine like terms: 20.934421415 + -2.5 = 18.434421415 x = 18.434421415 Simplifying x = 18.434421415Subproblem 2
x + 2.5 = -20.934421415 Simplifying x + 2.5 = -20.934421415 Reorder the terms: 2.5 + x = -20.934421415 Solving 2.5 + x = -20.934421415 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 = -20.934421415 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -20.934421415 + -2.5 x = -20.934421415 + -2.5 Combine like terms: -20.934421415 + -2.5 = -23.434421415 x = -23.434421415 Simplifying x = -23.434421415Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.434421415, -23.434421415}
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