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Simplifying 4x2 + 14x + -49 = 0 Reorder the terms: -49 + 14x + 4x2 = 0 Solving -49 + 14x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + 3.5x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + 3.5x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + 3.5x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + 3.5x + x2 = 0 + 12.25 3.5x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 3.5x + x2 = 12.25 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 12.25 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 12.25 + 3.0625 Combine like terms: 12.25 + 3.0625 = 15.3125 3.0625 + 3.5x + x2 = 15.3125 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 15.3125 Calculate the square root of the right side: 3.913118961 Break this problem into two subproblems by setting (x + 1.75) equal to 3.913118961 and -3.913118961.Subproblem 1
x + 1.75 = 3.913118961 Simplifying x + 1.75 = 3.913118961 Reorder the terms: 1.75 + x = 3.913118961 Solving 1.75 + x = 3.913118961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.913118961 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.913118961 + -1.75 x = 3.913118961 + -1.75 Combine like terms: 3.913118961 + -1.75 = 2.163118961 x = 2.163118961 Simplifying x = 2.163118961Subproblem 2
x + 1.75 = -3.913118961 Simplifying x + 1.75 = -3.913118961 Reorder the terms: 1.75 + x = -3.913118961 Solving 1.75 + x = -3.913118961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.913118961 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.913118961 + -1.75 x = -3.913118961 + -1.75 Combine like terms: -3.913118961 + -1.75 = -5.663118961 x = -5.663118961 Simplifying x = -5.663118961Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.163118961, -5.663118961}
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