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Simplifying 8x2 + 4x = 543 Reorder the terms: 4x + 8x2 = 543 Solving 4x + 8x2 = 543 Solving for variable 'x'. Reorder the terms: -543 + 4x + 8x2 = 543 + -543 Combine like terms: 543 + -543 = 0 -543 + 4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -67.875 + 0.5x + x2 = 0 Move the constant term to the right: Add '67.875' to each side of the equation. -67.875 + 0.5x + 67.875 + x2 = 0 + 67.875 Reorder the terms: -67.875 + 67.875 + 0.5x + x2 = 0 + 67.875 Combine like terms: -67.875 + 67.875 = 0.000 0.000 + 0.5x + x2 = 0 + 67.875 0.5x + x2 = 0 + 67.875 Combine like terms: 0 + 67.875 = 67.875 0.5x + x2 = 67.875 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 67.875 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 67.875 + 0.0625 Combine like terms: 67.875 + 0.0625 = 67.9375 0.0625 + 0.5x + x2 = 67.9375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 67.9375 Calculate the square root of the right side: 8.242420761 Break this problem into two subproblems by setting (x + 0.25) equal to 8.242420761 and -8.242420761.Subproblem 1
x + 0.25 = 8.242420761 Simplifying x + 0.25 = 8.242420761 Reorder the terms: 0.25 + x = 8.242420761 Solving 0.25 + x = 8.242420761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 8.242420761 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 8.242420761 + -0.25 x = 8.242420761 + -0.25 Combine like terms: 8.242420761 + -0.25 = 7.992420761 x = 7.992420761 Simplifying x = 7.992420761Subproblem 2
x + 0.25 = -8.242420761 Simplifying x + 0.25 = -8.242420761 Reorder the terms: 0.25 + x = -8.242420761 Solving 0.25 + x = -8.242420761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -8.242420761 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -8.242420761 + -0.25 x = -8.242420761 + -0.25 Combine like terms: -8.242420761 + -0.25 = -8.492420761 x = -8.492420761 Simplifying x = -8.492420761Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.992420761, -8.492420761}
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