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Simplifying 24x + x2 = -1 Solving 24x + x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 24x + x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 24x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 24x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 24x + x2 = 0 + -1 24x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 24x + x2 = -1 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 = -1 + 144 Reorder the terms: 144 + 24x + x2 = -1 + 144 Combine like terms: -1 + 144 = 143 144 + 24x + x2 = 143 Factor a perfect square on the left side: (x + 12)(x + 12) = 143 Calculate the square root of the right side: 11.958260743 Break this problem into two subproblems by setting (x + 12) equal to 11.958260743 and -11.958260743.Subproblem 1
x + 12 = 11.958260743 Simplifying x + 12 = 11.958260743 Reorder the terms: 12 + x = 11.958260743 Solving 12 + x = 11.958260743 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 = 11.958260743 + -12 Combine like terms: 12 + -12 = 0 0 + x = 11.958260743 + -12 x = 11.958260743 + -12 Combine like terms: 11.958260743 + -12 = -0.041739257 x = -0.041739257 Simplifying x = -0.041739257Subproblem 2
x + 12 = -11.958260743 Simplifying x + 12 = -11.958260743 Reorder the terms: 12 + x = -11.958260743 Solving 12 + x = -11.958260743 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 = -11.958260743 + -12 Combine like terms: 12 + -12 = 0 0 + x = -11.958260743 + -12 x = -11.958260743 + -12 Combine like terms: -11.958260743 + -12 = -23.958260743 x = -23.958260743 Simplifying x = -23.958260743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.041739257, -23.958260743}
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