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Simplifying 3x2 + -26x + 2 = 5x2 + 1 Reorder the terms: 2 + -26x + 3x2 = 5x2 + 1 Reorder the terms: 2 + -26x + 3x2 = 1 + 5x2 Solving 2 + -26x + 3x2 = 1 + 5x2 Solving for variable 'x'. Reorder the terms: 2 + -1 + -26x + 3x2 + -5x2 = 1 + 5x2 + -1 + -5x2 Combine like terms: 2 + -1 = 1 1 + -26x + 3x2 + -5x2 = 1 + 5x2 + -1 + -5x2 Combine like terms: 3x2 + -5x2 = -2x2 1 + -26x + -2x2 = 1 + 5x2 + -1 + -5x2 Reorder the terms: 1 + -26x + -2x2 = 1 + -1 + 5x2 + -5x2 Combine like terms: 1 + -1 = 0 1 + -26x + -2x2 = 0 + 5x2 + -5x2 1 + -26x + -2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 1 + -26x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 13x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 13x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 13x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 13x + x2 = 0 + 0.5 13x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 13x + x2 = 0.5 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 0.5 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 0.5 + 42.25 Combine like terms: 0.5 + 42.25 = 42.75 42.25 + 13x + x2 = 42.75 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 42.75 Calculate the square root of the right side: 6.538348415 Break this problem into two subproblems by setting (x + 6.5) equal to 6.538348415 and -6.538348415.Subproblem 1
x + 6.5 = 6.538348415 Simplifying x + 6.5 = 6.538348415 Reorder the terms: 6.5 + x = 6.538348415 Solving 6.5 + x = 6.538348415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 6.538348415 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.538348415 + -6.5 x = 6.538348415 + -6.5 Combine like terms: 6.538348415 + -6.5 = 0.038348415 x = 0.038348415 Simplifying x = 0.038348415Subproblem 2
x + 6.5 = -6.538348415 Simplifying x + 6.5 = -6.538348415 Reorder the terms: 6.5 + x = -6.538348415 Solving 6.5 + x = -6.538348415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -6.538348415 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.538348415 + -6.5 x = -6.538348415 + -6.5 Combine like terms: -6.538348415 + -6.5 = -13.038348415 x = -13.038348415 Simplifying x = -13.038348415Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.038348415, -13.038348415}
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