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Simplifying 3x2 + -26x + 2 = 5x2 + 1x Reorder the terms: 2 + -26x + 3x2 = 5x2 + 1x Reorder the terms: 2 + -26x + 3x2 = 1x + 5x2 Solving 2 + -26x + 3x2 = 1x + 5x2 Solving for variable 'x'. Reorder the terms: 2 + -26x + -1x + 3x2 + -5x2 = 1x + 5x2 + -1x + -5x2 Combine like terms: -26x + -1x = -27x 2 + -27x + 3x2 + -5x2 = 1x + 5x2 + -1x + -5x2 Combine like terms: 3x2 + -5x2 = -2x2 2 + -27x + -2x2 = 1x + 5x2 + -1x + -5x2 Reorder the terms: 2 + -27x + -2x2 = 1x + -1x + 5x2 + -5x2 Combine like terms: 1x + -1x = 0 2 + -27x + -2x2 = 0 + 5x2 + -5x2 2 + -27x + -2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 2 + -27x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + 13.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 13.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 13.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 13.5x + x2 = 0 + 1 13.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 13.5x + x2 = 1 The x term is 13.5x. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5x + 45.5625 + x2 = 1 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = 1 + 45.5625 Combine like terms: 1 + 45.5625 = 46.5625 45.5625 + 13.5x + x2 = 46.5625 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 46.5625 Calculate the square root of the right side: 6.823672032 Break this problem into two subproblems by setting (x + 6.75) equal to 6.823672032 and -6.823672032.Subproblem 1
x + 6.75 = 6.823672032 Simplifying x + 6.75 = 6.823672032 Reorder the terms: 6.75 + x = 6.823672032 Solving 6.75 + x = 6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = 6.823672032 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 6.823672032 + -6.75 x = 6.823672032 + -6.75 Combine like terms: 6.823672032 + -6.75 = 0.073672032 x = 0.073672032 Simplifying x = 0.073672032Subproblem 2
x + 6.75 = -6.823672032 Simplifying x + 6.75 = -6.823672032 Reorder the terms: 6.75 + x = -6.823672032 Solving 6.75 + x = -6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = -6.823672032 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -6.823672032 + -6.75 x = -6.823672032 + -6.75 Combine like terms: -6.823672032 + -6.75 = -13.573672032 x = -13.573672032 Simplifying x = -13.573672032Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.073672032, -13.573672032}
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