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Simplifying 2x2 + 14x + -71 = 0 Reorder the terms: -71 + 14x + 2x2 = 0 Solving -71 + 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'. -35.5 + 7x + x2 = 0 Move the constant term to the right: Add '35.5' to each side of the equation. -35.5 + 7x + 35.5 + x2 = 0 + 35.5 Reorder the terms: -35.5 + 35.5 + 7x + x2 = 0 + 35.5 Combine like terms: -35.5 + 35.5 = 0.0 0.0 + 7x + x2 = 0 + 35.5 7x + x2 = 0 + 35.5 Combine like terms: 0 + 35.5 = 35.5 7x + x2 = 35.5 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 = 35.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 35.5 + 12.25 Combine like terms: 35.5 + 12.25 = 47.75 12.25 + 7x + x2 = 47.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 47.75 Calculate the square root of the right side: 6.910137481 Break this problem into two subproblems by setting (x + 3.5) equal to 6.910137481 and -6.910137481.Subproblem 1
x + 3.5 = 6.910137481 Simplifying x + 3.5 = 6.910137481 Reorder the terms: 3.5 + x = 6.910137481 Solving 3.5 + x = 6.910137481 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 = 6.910137481 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.910137481 + -3.5 x = 6.910137481 + -3.5 Combine like terms: 6.910137481 + -3.5 = 3.410137481 x = 3.410137481 Simplifying x = 3.410137481Subproblem 2
x + 3.5 = -6.910137481 Simplifying x + 3.5 = -6.910137481 Reorder the terms: 3.5 + x = -6.910137481 Solving 3.5 + x = -6.910137481 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 = -6.910137481 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.910137481 + -3.5 x = -6.910137481 + -3.5 Combine like terms: -6.910137481 + -3.5 = -10.410137481 x = -10.410137481 Simplifying x = -10.410137481Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.410137481, -10.410137481}
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