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Simplifying 5.5x2 + 44x + -160 = 0 Reorder the terms: -160 + 44x + 5.5x2 = 0 Solving -160 + 44x + 5.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.5 the coefficient of the squared term: Divide each side by '5.5'. -29.09090909 + 8x + x2 = 0 Move the constant term to the right: Add '29.09090909' to each side of the equation. -29.09090909 + 8x + 29.09090909 + x2 = 0 + 29.09090909 Reorder the terms: -29.09090909 + 29.09090909 + 8x + x2 = 0 + 29.09090909 Combine like terms: -29.09090909 + 29.09090909 = 0.00000000 0.00000000 + 8x + x2 = 0 + 29.09090909 8x + x2 = 0 + 29.09090909 Combine like terms: 0 + 29.09090909 = 29.09090909 8x + x2 = 29.09090909 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 = 29.09090909 + 16 Reorder the terms: 16 + 8x + x2 = 29.09090909 + 16 Combine like terms: 29.09090909 + 16 = 45.09090909 16 + 8x + x2 = 45.09090909 Factor a perfect square on the left side: (x + 4)(x + 4) = 45.09090909 Calculate the square root of the right side: 6.714976477 Break this problem into two subproblems by setting (x + 4) equal to 6.714976477 and -6.714976477.Subproblem 1
x + 4 = 6.714976477 Simplifying x + 4 = 6.714976477 Reorder the terms: 4 + x = 6.714976477 Solving 4 + x = 6.714976477 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 = 6.714976477 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.714976477 + -4 x = 6.714976477 + -4 Combine like terms: 6.714976477 + -4 = 2.714976477 x = 2.714976477 Simplifying x = 2.714976477Subproblem 2
x + 4 = -6.714976477 Simplifying x + 4 = -6.714976477 Reorder the terms: 4 + x = -6.714976477 Solving 4 + x = -6.714976477 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 = -6.714976477 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.714976477 + -4 x = -6.714976477 + -4 Combine like terms: -6.714976477 + -4 = -10.714976477 x = -10.714976477 Simplifying x = -10.714976477Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.714976477, -10.714976477}
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