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Simplifying 2x2 = 14x + 49 Reorder the terms: 2x2 = 49 + 14x Solving 2x2 = 49 + 14x Solving for variable 'x'. Reorder the terms: -49 + -14x + 2x2 = 49 + 14x + -49 + -14x Reorder the terms: -49 + -14x + 2x2 = 49 + -49 + 14x + -14x Combine like terms: 49 + -49 = 0 -49 + -14x + 2x2 = 0 + 14x + -14x -49 + -14x + 2x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -49 + -14x + 2x2 = 0 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 = 9.562177826 x = 9.562177826 Simplifying x = 9.562177826Subproblem 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 = -2.562177826 x = -2.562177826 Simplifying x = -2.562177826Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.562177826, -2.562177826}
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