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Simplifying 7(12x * 3) * 7x = 36 + 56347x Reorder the terms for easier multiplication: 7(12 * 3x) * 7x = 36 + 56347x Multiply 12 * 3 7(36x) * 7x = 36 + 56347x Remove parenthesis around (36x) 7 * 36x * 7x = 36 + 56347x Reorder the terms for easier multiplication: 7 * 36 * 7x * x = 36 + 56347x Multiply 7 * 36 252 * 7x * x = 36 + 56347x Multiply 252 * 7 1764x * x = 36 + 56347x Multiply x * x 1764x2 = 36 + 56347x Solving 1764x2 = 36 + 56347x Solving for variable 'x'. Reorder the terms: -36 + -56347x + 1764x2 = 36 + 56347x + -36 + -56347x Reorder the terms: -36 + -56347x + 1764x2 = 36 + -36 + 56347x + -56347x Combine like terms: 36 + -36 = 0 -36 + -56347x + 1764x2 = 0 + 56347x + -56347x -36 + -56347x + 1764x2 = 56347x + -56347x Combine like terms: 56347x + -56347x = 0 -36 + -56347x + 1764x2 = 0 Begin completing the square. Divide all terms by 1764 the coefficient of the squared term: Divide each side by '1764'. -0.02040816327 + -31.94274376x + x2 = 0 Move the constant term to the right: Add '0.02040816327' to each side of the equation. -0.02040816327 + -31.94274376x + 0.02040816327 + x2 = 0 + 0.02040816327 Reorder the terms: -0.02040816327 + 0.02040816327 + -31.94274376x + x2 = 0 + 0.02040816327 Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000 0.00000000000 + -31.94274376x + x2 = 0 + 0.02040816327 -31.94274376x + x2 = 0 + 0.02040816327 Combine like terms: 0 + 0.02040816327 = 0.02040816327 -31.94274376x + x2 = 0.02040816327 The x term is -31.94274376x. Take half its coefficient (-15.97137188). Square it (255.0847197) and add it to both sides. Add '255.0847197' to each side of the equation. -31.94274376x + 255.0847197 + x2 = 0.02040816327 + 255.0847197 Reorder the terms: 255.0847197 + -31.94274376x + x2 = 0.02040816327 + 255.0847197 Combine like terms: 0.02040816327 + 255.0847197 = 255.10512786327 255.0847197 + -31.94274376x + x2 = 255.10512786327 Factor a perfect square on the left side: (x + -15.97137188)(x + -15.97137188) = 255.10512786327 Calculate the square root of the right side: 15.972010765 Break this problem into two subproblems by setting (x + -15.97137188) equal to 15.972010765 and -15.972010765.Subproblem 1
x + -15.97137188 = 15.972010765 Simplifying x + -15.97137188 = 15.972010765 Reorder the terms: -15.97137188 + x = 15.972010765 Solving -15.97137188 + x = 15.972010765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.97137188' to each side of the equation. -15.97137188 + 15.97137188 + x = 15.972010765 + 15.97137188 Combine like terms: -15.97137188 + 15.97137188 = 0.00000000 0.00000000 + x = 15.972010765 + 15.97137188 x = 15.972010765 + 15.97137188 Combine like terms: 15.972010765 + 15.97137188 = 31.943382645 x = 31.943382645 Simplifying x = 31.943382645Subproblem 2
x + -15.97137188 = -15.972010765 Simplifying x + -15.97137188 = -15.972010765 Reorder the terms: -15.97137188 + x = -15.972010765 Solving -15.97137188 + x = -15.972010765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.97137188' to each side of the equation. -15.97137188 + 15.97137188 + x = -15.972010765 + 15.97137188 Combine like terms: -15.97137188 + 15.97137188 = 0.00000000 0.00000000 + x = -15.972010765 + 15.97137188 x = -15.972010765 + 15.97137188 Combine like terms: -15.972010765 + 15.97137188 = -0.000638885 x = -0.000638885 Simplifying x = -0.000638885Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.943382645, -0.000638885}
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