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Simplifying 5x2 + 27x = 14 + -13x Reorder the terms: 27x + 5x2 = 14 + -13x Solving 27x + 5x2 = 14 + -13x Solving for variable 'x'. Reorder the terms: -14 + 27x + 13x + 5x2 = 14 + -13x + -14 + 13x Combine like terms: 27x + 13x = 40x -14 + 40x + 5x2 = 14 + -13x + -14 + 13x Reorder the terms: -14 + 40x + 5x2 = 14 + -14 + -13x + 13x Combine like terms: 14 + -14 = 0 -14 + 40x + 5x2 = 0 + -13x + 13x -14 + 40x + 5x2 = -13x + 13x Combine like terms: -13x + 13x = 0 -14 + 40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + 8x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 8x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 8x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 8x + x2 = 0 + 2.8 8x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 8x + x2 = 2.8 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 2.8 + 16 Reorder the terms: 16 + 8x + x2 = 2.8 + 16 Combine like terms: 2.8 + 16 = 18.8 16 + 8x + x2 = 18.8 Factor a perfect square on the left side: (x + 4)(x + 4) = 18.8 Calculate the square root of the right side: 4.335896678 Break this problem into two subproblems by setting (x + 4) equal to 4.335896678 and -4.335896678.Subproblem 1
x + 4 = 4.335896678 Simplifying x + 4 = 4.335896678 Reorder the terms: 4 + x = 4.335896678 Solving 4 + x = 4.335896678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.335896678 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.335896678 + -4 x = 4.335896678 + -4 Combine like terms: 4.335896678 + -4 = 0.335896678 x = 0.335896678 Simplifying x = 0.335896678Subproblem 2
x + 4 = -4.335896678 Simplifying x + 4 = -4.335896678 Reorder the terms: 4 + x = -4.335896678 Solving 4 + x = -4.335896678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.335896678 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.335896678 + -4 x = -4.335896678 + -4 Combine like terms: -4.335896678 + -4 = -8.335896678 x = -8.335896678 Simplifying x = -8.335896678Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.335896678, -8.335896678}
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