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Simplifying 24x + x2 = 100 Solving 24x + x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 24x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 24x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 24x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 24x + x2 = 0 + 100 24x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 24x + x2 = 100 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 = 100 + 144 Reorder the terms: 144 + 24x + x2 = 100 + 144 Combine like terms: 100 + 144 = 244 144 + 24x + x2 = 244 Factor a perfect square on the left side: (x + 12)(x + 12) = 244 Calculate the square root of the right side: 15.620499352 Break this problem into two subproblems by setting (x + 12) equal to 15.620499352 and -15.620499352.Subproblem 1
x + 12 = 15.620499352 Simplifying x + 12 = 15.620499352 Reorder the terms: 12 + x = 15.620499352 Solving 12 + x = 15.620499352 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 = 15.620499352 + -12 Combine like terms: 12 + -12 = 0 0 + x = 15.620499352 + -12 x = 15.620499352 + -12 Combine like terms: 15.620499352 + -12 = 3.620499352 x = 3.620499352 Simplifying x = 3.620499352Subproblem 2
x + 12 = -15.620499352 Simplifying x + 12 = -15.620499352 Reorder the terms: 12 + x = -15.620499352 Solving 12 + x = -15.620499352 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 = -15.620499352 + -12 Combine like terms: 12 + -12 = 0 0 + x = -15.620499352 + -12 x = -15.620499352 + -12 Combine like terms: -15.620499352 + -12 = -27.620499352 x = -27.620499352 Simplifying x = -27.620499352Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.620499352, -27.620499352}
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