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Simplifying 4x2 + 47x + 103 = 0 Reorder the terms: 103 + 47x + 4x2 = 0 Solving 103 + 47x + 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'. 25.75 + 11.75x + x2 = 0 Move the constant term to the right: Add '-25.75' to each side of the equation. 25.75 + 11.75x + -25.75 + x2 = 0 + -25.75 Reorder the terms: 25.75 + -25.75 + 11.75x + x2 = 0 + -25.75 Combine like terms: 25.75 + -25.75 = 0.00 0.00 + 11.75x + x2 = 0 + -25.75 11.75x + x2 = 0 + -25.75 Combine like terms: 0 + -25.75 = -25.75 11.75x + x2 = -25.75 The x term is 11.75x. Take half its coefficient (5.875). Square it (34.515625) and add it to both sides. Add '34.515625' to each side of the equation. 11.75x + 34.515625 + x2 = -25.75 + 34.515625 Reorder the terms: 34.515625 + 11.75x + x2 = -25.75 + 34.515625 Combine like terms: -25.75 + 34.515625 = 8.765625 34.515625 + 11.75x + x2 = 8.765625 Factor a perfect square on the left side: (x + 5.875)(x + 5.875) = 8.765625 Calculate the square root of the right side: 2.960679821 Break this problem into two subproblems by setting (x + 5.875) equal to 2.960679821 and -2.960679821.Subproblem 1
x + 5.875 = 2.960679821 Simplifying x + 5.875 = 2.960679821 Reorder the terms: 5.875 + x = 2.960679821 Solving 5.875 + x = 2.960679821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.875' to each side of the equation. 5.875 + -5.875 + x = 2.960679821 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + x = 2.960679821 + -5.875 x = 2.960679821 + -5.875 Combine like terms: 2.960679821 + -5.875 = -2.914320179 x = -2.914320179 Simplifying x = -2.914320179Subproblem 2
x + 5.875 = -2.960679821 Simplifying x + 5.875 = -2.960679821 Reorder the terms: 5.875 + x = -2.960679821 Solving 5.875 + x = -2.960679821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.875' to each side of the equation. 5.875 + -5.875 + x = -2.960679821 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + x = -2.960679821 + -5.875 x = -2.960679821 + -5.875 Combine like terms: -2.960679821 + -5.875 = -8.835679821 x = -8.835679821 Simplifying x = -8.835679821Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.914320179, -8.835679821}
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