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Simplifying 8x2 + 18x + 3 = 0 Reorder the terms: 3 + 18x + 8x2 = 0 Solving 3 + 18x + 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'. 0.375 + 2.25x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 2.25x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 2.25x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 2.25x + x2 = 0 + -0.375 2.25x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 2.25x + x2 = -0.375 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -0.375 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -0.375 + 1.265625 Combine like terms: -0.375 + 1.265625 = 0.890625 1.265625 + 2.25x + x2 = 0.890625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + 1.125) equal to 0.943729304 and -0.943729304.Subproblem 1
x + 1.125 = 0.943729304 Simplifying x + 1.125 = 0.943729304 Reorder the terms: 1.125 + x = 0.943729304 Solving 1.125 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 0.943729304 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 0.943729304 + -1.125 x = 0.943729304 + -1.125 Combine like terms: 0.943729304 + -1.125 = -0.181270696 x = -0.181270696 Simplifying x = -0.181270696Subproblem 2
x + 1.125 = -0.943729304 Simplifying x + 1.125 = -0.943729304 Reorder the terms: 1.125 + x = -0.943729304 Solving 1.125 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -0.943729304 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -0.943729304 + -1.125 x = -0.943729304 + -1.125 Combine like terms: -0.943729304 + -1.125 = -2.068729304 x = -2.068729304 Simplifying x = -2.068729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.181270696, -2.068729304}
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