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Simplifying 49x2 + 56x + -32 = 0 Reorder the terms: -32 + 56x + 49x2 = 0 Solving -32 + 56x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.6530612245 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '0.6530612245' to each side of the equation. -0.6530612245 + 1.142857143x + 0.6530612245 + x2 = 0 + 0.6530612245 Reorder the terms: -0.6530612245 + 0.6530612245 + 1.142857143x + x2 = 0 + 0.6530612245 Combine like terms: -0.6530612245 + 0.6530612245 = 0.0000000000 0.0000000000 + 1.142857143x + x2 = 0 + 0.6530612245 1.142857143x + x2 = 0 + 0.6530612245 Combine like terms: 0 + 0.6530612245 = 0.6530612245 1.142857143x + x2 = 0.6530612245 The x term is 1.142857143x. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143x + 0.3265306123 + x2 = 0.6530612245 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = 0.6530612245 + 0.3265306123 Combine like terms: 0.6530612245 + 0.3265306123 = 0.9795918368 0.3265306123 + 1.142857143x + x2 = 0.9795918368 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = 0.9795918368 Calculate the square root of the right side: 0.989743319 Break this problem into two subproblems by setting (x + 0.5714285715) equal to 0.989743319 and -0.989743319.Subproblem 1
x + 0.5714285715 = 0.989743319 Simplifying x + 0.5714285715 = 0.989743319 Reorder the terms: 0.5714285715 + x = 0.989743319 Solving 0.5714285715 + x = 0.989743319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = 0.989743319 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 0.989743319 + -0.5714285715 x = 0.989743319 + -0.5714285715 Combine like terms: 0.989743319 + -0.5714285715 = 0.4183147475 x = 0.4183147475 Simplifying x = 0.4183147475Subproblem 2
x + 0.5714285715 = -0.989743319 Simplifying x + 0.5714285715 = -0.989743319 Reorder the terms: 0.5714285715 + x = -0.989743319 Solving 0.5714285715 + x = -0.989743319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = -0.989743319 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -0.989743319 + -0.5714285715 x = -0.989743319 + -0.5714285715 Combine like terms: -0.989743319 + -0.5714285715 = -1.5611718905 x = -1.5611718905 Simplifying x = -1.5611718905Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4183147475, -1.5611718905}
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