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Simplifying 2x(2x) = 13x + 1 Remove parenthesis around (2x) 2x * 2x = 13x + 1 Reorder the terms for easier multiplication: 2 * 2x * x = 13x + 1 Multiply 2 * 2 4x * x = 13x + 1 Multiply x * x 4x2 = 13x + 1 Reorder the terms: 4x2 = 1 + 13x Solving 4x2 = 1 + 13x Solving for variable 'x'. Reorder the terms: -1 + -13x + 4x2 = 1 + 13x + -1 + -13x Reorder the terms: -1 + -13x + 4x2 = 1 + -1 + 13x + -13x Combine like terms: 1 + -1 = 0 -1 + -13x + 4x2 = 0 + 13x + -13x -1 + -13x + 4x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -1 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -3.25x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -3.25x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -3.25x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -3.25x + x2 = 0 + 0.25 -3.25x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -3.25x + x2 = 0.25 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 0.25 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 0.25 + 2.640625 Combine like terms: 0.25 + 2.640625 = 2.890625 2.640625 + -3.25x + x2 = 2.890625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + -1.625) equal to 1.700183814 and -1.700183814.Subproblem 1
x + -1.625 = 1.700183814 Simplifying x + -1.625 = 1.700183814 Reorder the terms: -1.625 + x = 1.700183814 Solving -1.625 + x = 1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.700183814 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.700183814 + 1.625 x = 1.700183814 + 1.625 Combine like terms: 1.700183814 + 1.625 = 3.325183814 x = 3.325183814 Simplifying x = 3.325183814Subproblem 2
x + -1.625 = -1.700183814 Simplifying x + -1.625 = -1.700183814 Reorder the terms: -1.625 + x = -1.700183814 Solving -1.625 + x = -1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.700183814 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.700183814 + 1.625 x = -1.700183814 + 1.625 Combine like terms: -1.700183814 + 1.625 = -0.075183814 x = -0.075183814 Simplifying x = -0.075183814Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.325183814, -0.075183814}
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