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Simplifying 2x2 + 4x + -49 = 0 Reorder the terms: -49 + 4x + 2x2 = 0 Solving -49 + 4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24.5 + 2x + x2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + 2x + 24.5 + x2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + 2x + x2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + 2x + x2 = 0 + 24.5 2x + x2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 2x + x2 = 24.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 24.5 + 1 Reorder the terms: 1 + 2x + x2 = 24.5 + 1 Combine like terms: 24.5 + 1 = 25.5 1 + 2x + x2 = 25.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 25.5 Calculate the square root of the right side: 5.049752469 Break this problem into two subproblems by setting (x + 1) equal to 5.049752469 and -5.049752469.Subproblem 1
x + 1 = 5.049752469 Simplifying x + 1 = 5.049752469 Reorder the terms: 1 + x = 5.049752469 Solving 1 + x = 5.049752469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.049752469 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.049752469 + -1 x = 5.049752469 + -1 Combine like terms: 5.049752469 + -1 = 4.049752469 x = 4.049752469 Simplifying x = 4.049752469Subproblem 2
x + 1 = -5.049752469 Simplifying x + 1 = -5.049752469 Reorder the terms: 1 + x = -5.049752469 Solving 1 + x = -5.049752469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.049752469 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.049752469 + -1 x = -5.049752469 + -1 Combine like terms: -5.049752469 + -1 = -6.049752469 x = -6.049752469 Simplifying x = -6.049752469Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.049752469, -6.049752469}
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