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Simplifying 24x + x2 = 493 Solving 24x + x2 = 493 Solving for variable 'x'. Reorder the terms: -493 + 24x + x2 = 493 + -493 Combine like terms: 493 + -493 = 0 -493 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '493' to each side of the equation. -493 + 24x + 493 + x2 = 0 + 493 Reorder the terms: -493 + 493 + 24x + x2 = 0 + 493 Combine like terms: -493 + 493 = 0 0 + 24x + x2 = 0 + 493 24x + x2 = 0 + 493 Combine like terms: 0 + 493 = 493 24x + x2 = 493 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 493 + 144 Reorder the terms: 144 + 24x + x2 = 493 + 144 Combine like terms: 493 + 144 = 637 144 + 24x + x2 = 637 Factor a perfect square on the left side: (x + 12)(x + 12) = 637 Calculate the square root of the right side: 25.238858928 Break this problem into two subproblems by setting (x + 12) equal to 25.238858928 and -25.238858928.Subproblem 1
x + 12 = 25.238858928 Simplifying x + 12 = 25.238858928 Reorder the terms: 12 + x = 25.238858928 Solving 12 + x = 25.238858928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 25.238858928 + -12 Combine like terms: 12 + -12 = 0 0 + x = 25.238858928 + -12 x = 25.238858928 + -12 Combine like terms: 25.238858928 + -12 = 13.238858928 x = 13.238858928 Simplifying x = 13.238858928Subproblem 2
x + 12 = -25.238858928 Simplifying x + 12 = -25.238858928 Reorder the terms: 12 + x = -25.238858928 Solving 12 + x = -25.238858928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -25.238858928 + -12 Combine like terms: 12 + -12 = 0 0 + x = -25.238858928 + -12 x = -25.238858928 + -12 Combine like terms: -25.238858928 + -12 = -37.238858928 x = -37.238858928 Simplifying x = -37.238858928Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.238858928, -37.238858928}
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