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Simplifying x2 + -27x = x + 1 Reorder the terms: -27x + x2 = x + 1 Reorder the terms: -27x + x2 = 1 + x Solving -27x + x2 = 1 + x Solving for variable 'x'. Reorder the terms: -1 + -27x + -1x + x2 = 1 + x + -1 + -1x Combine like terms: -27x + -1x = -28x -1 + -28x + x2 = 1 + x + -1 + -1x Reorder the terms: -1 + -28x + x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -1 + -28x + x2 = 0 + x + -1x -1 + -28x + x2 = x + -1x Combine like terms: x + -1x = 0 -1 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -28x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -28x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -28x + x2 = 0 + 1 -28x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -28x + x2 = 1 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = 1 + 196 Reorder the terms: 196 + -28x + x2 = 1 + 196 Combine like terms: 1 + 196 = 197 196 + -28x + x2 = 197 Factor a perfect square on the left side: (x + -14)(x + -14) = 197 Calculate the square root of the right side: 14.035668848 Break this problem into two subproblems by setting (x + -14) equal to 14.035668848 and -14.035668848.Subproblem 1
x + -14 = 14.035668848 Simplifying x + -14 = 14.035668848 Reorder the terms: -14 + x = 14.035668848 Solving -14 + x = 14.035668848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 14.035668848 + 14 Combine like terms: -14 + 14 = 0 0 + x = 14.035668848 + 14 x = 14.035668848 + 14 Combine like terms: 14.035668848 + 14 = 28.035668848 x = 28.035668848 Simplifying x = 28.035668848Subproblem 2
x + -14 = -14.035668848 Simplifying x + -14 = -14.035668848 Reorder the terms: -14 + x = -14.035668848 Solving -14 + x = -14.035668848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -14.035668848 + 14 Combine like terms: -14 + 14 = 0 0 + x = -14.035668848 + 14 x = -14.035668848 + 14 Combine like terms: -14.035668848 + 14 = -0.035668848 x = -0.035668848 Simplifying x = -0.035668848Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.035668848, -0.035668848}
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