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Simplifying (x * x) + 24x = 1 Multiply x * x (x2) + 24x = 1 x2 + 24x = 1 Reorder the terms: 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 = 145 144 + 24x + x2 = 145 Factor a perfect square on the left side: (x + 12)(x + 12) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + 12) equal to 12.041594579 and -12.041594579.Subproblem 1
x + 12 = 12.041594579 Simplifying x + 12 = 12.041594579 Reorder the terms: 12 + x = 12.041594579 Solving 12 + x = 12.041594579 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 = 12.041594579 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.041594579 + -12 x = 12.041594579 + -12 Combine like terms: 12.041594579 + -12 = 0.041594579 x = 0.041594579 Simplifying x = 0.041594579Subproblem 2
x + 12 = -12.041594579 Simplifying x + 12 = -12.041594579 Reorder the terms: 12 + x = -12.041594579 Solving 12 + x = -12.041594579 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 = -12.041594579 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.041594579 + -12 x = -12.041594579 + -12 Combine like terms: -12.041594579 + -12 = -24.041594579 x = -24.041594579 Simplifying x = -24.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.041594579, -24.041594579}
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