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Simplifying 2x2 + 14x + -49 = 0 Reorder the terms: -49 + 14x + 2x2 = 0 Solving -49 + 14x + 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 + 7x + x2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + 7x + 24.5 + x2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + 7x + x2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + 7x + x2 = 0 + 24.5 7x + x2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 7x + x2 = 24.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 24.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 24.5 + 12.25 Combine like terms: 24.5 + 12.25 = 36.75 12.25 + 7x + x2 = 36.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 36.75 Calculate the square root of the right side: 6.062177826 Break this problem into two subproblems by setting (x + 3.5) equal to 6.062177826 and -6.062177826.Subproblem 1
x + 3.5 = 6.062177826 Simplifying x + 3.5 = 6.062177826 Reorder the terms: 3.5 + x = 6.062177826 Solving 3.5 + x = 6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.062177826 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.062177826 + -3.5 x = 6.062177826 + -3.5 Combine like terms: 6.062177826 + -3.5 = 2.562177826 x = 2.562177826 Simplifying x = 2.562177826Subproblem 2
x + 3.5 = -6.062177826 Simplifying x + 3.5 = -6.062177826 Reorder the terms: 3.5 + x = -6.062177826 Solving 3.5 + x = -6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.062177826 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.062177826 + -3.5 x = -6.062177826 + -3.5 Combine like terms: -6.062177826 + -3.5 = -9.562177826 x = -9.562177826 Simplifying x = -9.562177826Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.562177826, -9.562177826}
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