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Simplifying x2 + 24x = 9 Reorder the terms: 24x + x2 = 9 Solving 24x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 24x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 24x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 24x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 24x + x2 = 0 + 9 24x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 24x + x2 = 9 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 = 9 + 144 Reorder the terms: 144 + 24x + x2 = 9 + 144 Combine like terms: 9 + 144 = 153 144 + 24x + x2 = 153 Factor a perfect square on the left side: (x + 12)(x + 12) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + 12) equal to 12.369316877 and -12.369316877.Subproblem 1
x + 12 = 12.369316877 Simplifying x + 12 = 12.369316877 Reorder the terms: 12 + x = 12.369316877 Solving 12 + x = 12.369316877 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 = 12.369316877 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.369316877 + -12 x = 12.369316877 + -12 Combine like terms: 12.369316877 + -12 = 0.369316877 x = 0.369316877 Simplifying x = 0.369316877Subproblem 2
x + 12 = -12.369316877 Simplifying x + 12 = -12.369316877 Reorder the terms: 12 + x = -12.369316877 Solving 12 + x = -12.369316877 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 = -12.369316877 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.369316877 + -12 x = -12.369316877 + -12 Combine like terms: -12.369316877 + -12 = -24.369316877 x = -24.369316877 Simplifying x = -24.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.369316877, -24.369316877}
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