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Simplifying 8x2 + 47x + 28 = 0 Reorder the terms: 28 + 47x + 8x2 = 0 Solving 28 + 47x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.5 + 5.875x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 5.875x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 5.875x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 5.875x + x2 = 0 + -3.5 5.875x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 5.875x + x2 = -3.5 The x term is 5.875x. Take half its coefficient (2.9375). Square it (8.62890625) and add it to both sides. Add '8.62890625' to each side of the equation. 5.875x + 8.62890625 + x2 = -3.5 + 8.62890625 Reorder the terms: 8.62890625 + 5.875x + x2 = -3.5 + 8.62890625 Combine like terms: -3.5 + 8.62890625 = 5.12890625 8.62890625 + 5.875x + x2 = 5.12890625 Factor a perfect square on the left side: (x + 2.9375)(x + 2.9375) = 5.12890625 Calculate the square root of the right side: 2.264708866 Break this problem into two subproblems by setting (x + 2.9375) equal to 2.264708866 and -2.264708866.Subproblem 1
x + 2.9375 = 2.264708866 Simplifying x + 2.9375 = 2.264708866 Reorder the terms: 2.9375 + x = 2.264708866 Solving 2.9375 + x = 2.264708866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9375' to each side of the equation. 2.9375 + -2.9375 + x = 2.264708866 + -2.9375 Combine like terms: 2.9375 + -2.9375 = 0.0000 0.0000 + x = 2.264708866 + -2.9375 x = 2.264708866 + -2.9375 Combine like terms: 2.264708866 + -2.9375 = -0.672791134 x = -0.672791134 Simplifying x = -0.672791134Subproblem 2
x + 2.9375 = -2.264708866 Simplifying x + 2.9375 = -2.264708866 Reorder the terms: 2.9375 + x = -2.264708866 Solving 2.9375 + x = -2.264708866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9375' to each side of the equation. 2.9375 + -2.9375 + x = -2.264708866 + -2.9375 Combine like terms: 2.9375 + -2.9375 = 0.0000 0.0000 + x = -2.264708866 + -2.9375 x = -2.264708866 + -2.9375 Combine like terms: -2.264708866 + -2.9375 = -5.202208866 x = -5.202208866 Simplifying x = -5.202208866Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.672791134, -5.202208866}
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