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Simplifying x + x * x = 25x + 3 Multiply x * x x + x2 = 25x + 3 Reorder the terms: x + x2 = 3 + 25x Solving x + x2 = 3 + 25x Solving for variable 'x'. Reorder the terms: -3 + x + -25x + x2 = 3 + 25x + -3 + -25x Combine like terms: x + -25x = -24x -3 + -24x + x2 = 3 + 25x + -3 + -25x Reorder the terms: -3 + -24x + x2 = 3 + -3 + 25x + -25x Combine like terms: 3 + -3 = 0 -3 + -24x + x2 = 0 + 25x + -25x -3 + -24x + x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -3 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -24x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -24x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -24x + x2 = 0 + 3 -24x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -24x + x2 = 3 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 = 3 + 144 Reorder the terms: 144 + -24x + x2 = 3 + 144 Combine like terms: 3 + 144 = 147 144 + -24x + x2 = 147 Factor a perfect square on the left side: (x + -12)(x + -12) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (x + -12) equal to 12.124355653 and -12.124355653.Subproblem 1
x + -12 = 12.124355653 Simplifying x + -12 = 12.124355653 Reorder the terms: -12 + x = 12.124355653 Solving -12 + x = 12.124355653 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 = 12.124355653 + 12 Combine like terms: -12 + 12 = 0 0 + x = 12.124355653 + 12 x = 12.124355653 + 12 Combine like terms: 12.124355653 + 12 = 24.124355653 x = 24.124355653 Simplifying x = 24.124355653Subproblem 2
x + -12 = -12.124355653 Simplifying x + -12 = -12.124355653 Reorder the terms: -12 + x = -12.124355653 Solving -12 + x = -12.124355653 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 = -12.124355653 + 12 Combine like terms: -12 + 12 = 0 0 + x = -12.124355653 + 12 x = -12.124355653 + 12 Combine like terms: -12.124355653 + 12 = -0.124355653 x = -0.124355653 Simplifying x = -0.124355653Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.124355653, -0.124355653}
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