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Simplifying 2x2 + 14x + 17 = 0 Reorder the terms: 17 + 14x + 2x2 = 0 Solving 17 + 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'. 8.5 + 7x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 7x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 7x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 7x + x2 = 0 + -8.5 7x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 7x + x2 = -8.5 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 = -8.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -8.5 + 12.25 Combine like terms: -8.5 + 12.25 = 3.75 12.25 + 7x + x2 = 3.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + 3.5) equal to 1.936491673 and -1.936491673.Subproblem 1
x + 3.5 = 1.936491673 Simplifying x + 3.5 = 1.936491673 Reorder the terms: 3.5 + x = 1.936491673 Solving 3.5 + x = 1.936491673 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 = 1.936491673 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.936491673 + -3.5 x = 1.936491673 + -3.5 Combine like terms: 1.936491673 + -3.5 = -1.563508327 x = -1.563508327 Simplifying x = -1.563508327Subproblem 2
x + 3.5 = -1.936491673 Simplifying x + 3.5 = -1.936491673 Reorder the terms: 3.5 + x = -1.936491673 Solving 3.5 + x = -1.936491673 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 = -1.936491673 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.936491673 + -3.5 x = -1.936491673 + -3.5 Combine like terms: -1.936491673 + -3.5 = -5.436491673 x = -5.436491673 Simplifying x = -5.436491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.563508327, -5.436491673}
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