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Simplifying 14x2 + -7x + -5 = 0 Reorder the terms: -5 + -7x + 14x2 = 0 Solving -5 + -7x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.3571428571 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + -0.5x + 0.3571428571 + x2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + -0.5x + x2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + -0.5x + x2 = 0 + 0.3571428571 -0.5x + x2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 -0.5x + x2 = 0.3571428571 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.3571428571 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.3571428571 + 0.0625 Combine like terms: 0.3571428571 + 0.0625 = 0.4196428571 0.0625 + -0.5x + x2 = 0.4196428571 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.4196428571 Calculate the square root of the right side: 0.64779847 Break this problem into two subproblems by setting (x + -0.25) equal to 0.64779847 and -0.64779847.Subproblem 1
x + -0.25 = 0.64779847 Simplifying x + -0.25 = 0.64779847 Reorder the terms: -0.25 + x = 0.64779847 Solving -0.25 + x = 0.64779847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.64779847 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.64779847 + 0.25 x = 0.64779847 + 0.25 Combine like terms: 0.64779847 + 0.25 = 0.89779847 x = 0.89779847 Simplifying x = 0.89779847Subproblem 2
x + -0.25 = -0.64779847 Simplifying x + -0.25 = -0.64779847 Reorder the terms: -0.25 + x = -0.64779847 Solving -0.25 + x = -0.64779847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.64779847 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.64779847 + 0.25 x = -0.64779847 + 0.25 Combine like terms: -0.64779847 + 0.25 = -0.39779847 x = -0.39779847 Simplifying x = -0.39779847Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.89779847, -0.39779847}
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