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Simplifying 5x2 + 66x + -245 = 0 Reorder the terms: -245 + 66x + 5x2 = 0 Solving -245 + 66x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -49 + 13.2x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 13.2x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 13.2x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 13.2x + x2 = 0 + 49 13.2x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 13.2x + x2 = 49 The x term is 13.2x. Take half its coefficient (6.6). Square it (43.56) and add it to both sides. Add '43.56' to each side of the equation. 13.2x + 43.56 + x2 = 49 + 43.56 Reorder the terms: 43.56 + 13.2x + x2 = 49 + 43.56 Combine like terms: 49 + 43.56 = 92.56 43.56 + 13.2x + x2 = 92.56 Factor a perfect square on the left side: (x + 6.6)(x + 6.6) = 92.56 Calculate the square root of the right side: 9.620810777 Break this problem into two subproblems by setting (x + 6.6) equal to 9.620810777 and -9.620810777.Subproblem 1
x + 6.6 = 9.620810777 Simplifying x + 6.6 = 9.620810777 Reorder the terms: 6.6 + x = 9.620810777 Solving 6.6 + x = 9.620810777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = 9.620810777 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = 9.620810777 + -6.6 x = 9.620810777 + -6.6 Combine like terms: 9.620810777 + -6.6 = 3.020810777 x = 3.020810777 Simplifying x = 3.020810777Subproblem 2
x + 6.6 = -9.620810777 Simplifying x + 6.6 = -9.620810777 Reorder the terms: 6.6 + x = -9.620810777 Solving 6.6 + x = -9.620810777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = -9.620810777 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = -9.620810777 + -6.6 x = -9.620810777 + -6.6 Combine like terms: -9.620810777 + -6.6 = -16.220810777 x = -16.220810777 Simplifying x = -16.220810777Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.020810777, -16.220810777}
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