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Simplifying 35x2 + 34x + -14 = 0 Reorder the terms: -14 + 34x + 35x2 = 0 Solving -14 + 34x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.4 + 0.9714285714x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.9714285714x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.9714285714x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.9714285714x + x2 = 0 + 0.4 0.9714285714x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.9714285714x + x2 = 0.4 The x term is 0.9714285714x. Take half its coefficient (0.4857142857). Square it (0.2359183673) and add it to both sides. Add '0.2359183673' to each side of the equation. 0.9714285714x + 0.2359183673 + x2 = 0.4 + 0.2359183673 Reorder the terms: 0.2359183673 + 0.9714285714x + x2 = 0.4 + 0.2359183673 Combine like terms: 0.4 + 0.2359183673 = 0.6359183673 0.2359183673 + 0.9714285714x + x2 = 0.6359183673 Factor a perfect square on the left side: (x + 0.4857142857)(x + 0.4857142857) = 0.6359183673 Calculate the square root of the right side: 0.797444899 Break this problem into two subproblems by setting (x + 0.4857142857) equal to 0.797444899 and -0.797444899.Subproblem 1
x + 0.4857142857 = 0.797444899 Simplifying x + 0.4857142857 = 0.797444899 Reorder the terms: 0.4857142857 + x = 0.797444899 Solving 0.4857142857 + x = 0.797444899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4857142857' to each side of the equation. 0.4857142857 + -0.4857142857 + x = 0.797444899 + -0.4857142857 Combine like terms: 0.4857142857 + -0.4857142857 = 0.0000000000 0.0000000000 + x = 0.797444899 + -0.4857142857 x = 0.797444899 + -0.4857142857 Combine like terms: 0.797444899 + -0.4857142857 = 0.3117306133 x = 0.3117306133 Simplifying x = 0.3117306133Subproblem 2
x + 0.4857142857 = -0.797444899 Simplifying x + 0.4857142857 = -0.797444899 Reorder the terms: 0.4857142857 + x = -0.797444899 Solving 0.4857142857 + x = -0.797444899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4857142857' to each side of the equation. 0.4857142857 + -0.4857142857 + x = -0.797444899 + -0.4857142857 Combine like terms: 0.4857142857 + -0.4857142857 = 0.0000000000 0.0000000000 + x = -0.797444899 + -0.4857142857 x = -0.797444899 + -0.4857142857 Combine like terms: -0.797444899 + -0.4857142857 = -1.2831591847 x = -1.2831591847 Simplifying x = -1.2831591847Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3117306133, -1.2831591847}
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