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Simplifying 14x2 + 14x = 17 Reorder the terms: 14x + 14x2 = 17 Solving 14x + 14x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + 14x + 14x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 14x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.214285714 + x + x2 = 0 Move the constant term to the right: Add '1.214285714' to each side of the equation. -1.214285714 + x + 1.214285714 + x2 = 0 + 1.214285714 Reorder the terms: -1.214285714 + 1.214285714 + x + x2 = 0 + 1.214285714 Combine like terms: -1.214285714 + 1.214285714 = 0.000000000 0.000000000 + x + x2 = 0 + 1.214285714 x + x2 = 0 + 1.214285714 Combine like terms: 0 + 1.214285714 = 1.214285714 x + x2 = 1.214285714 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.214285714 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.214285714 + 0.25 Combine like terms: 1.214285714 + 0.25 = 1.464285714 1.25 + x2 = 1.464285714 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.464285714 Calculate the square root of the right side: 1.210076739 Break this problem into two subproblems by setting (x + 0.5) equal to 1.210076739 and -1.210076739.Subproblem 1
x + 0.5 = 1.210076739 Simplifying x + 0.5 = 1.210076739 Reorder the terms: 0.5 + x = 1.210076739 Solving 0.5 + x = 1.210076739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.210076739 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.210076739 + -0.5 x = 1.210076739 + -0.5 Combine like terms: 1.210076739 + -0.5 = 0.710076739 x = 0.710076739 Simplifying x = 0.710076739Subproblem 2
x + 0.5 = -1.210076739 Simplifying x + 0.5 = -1.210076739 Reorder the terms: 0.5 + x = -1.210076739 Solving 0.5 + x = -1.210076739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.210076739 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.210076739 + -0.5 x = -1.210076739 + -0.5 Combine like terms: -1.210076739 + -0.5 = -1.710076739 x = -1.710076739 Simplifying x = -1.710076739Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.710076739, -1.710076739}
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