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Simplifying 2x(6x + 7) + -5 = 0 Reorder the terms: 2x(7 + 6x) + -5 = 0 (7 * 2x + 6x * 2x) + -5 = 0 (14x + 12x2) + -5 = 0 Reorder the terms: -5 + 14x + 12x2 = 0 Solving -5 + 14x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + 1.166666667x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + 1.166666667x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + 1.166666667x + x2 = 0 + 0.4166666667 1.166666667x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 1.166666667x + x2 = 0.4166666667 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = 0.4166666667 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 0.4166666667 + 0.3402777780 Combine like terms: 0.4166666667 + 0.3402777780 = 0.7569444447 0.3402777780 + 1.166666667x + x2 = 0.7569444447 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 0.7569444447 Calculate the square root of the right side: 0.870025543 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 0.870025543 and -0.870025543.Subproblem 1
x + 0.5833333335 = 0.870025543 Simplifying x + 0.5833333335 = 0.870025543 Reorder the terms: 0.5833333335 + x = 0.870025543 Solving 0.5833333335 + x = 0.870025543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 0.870025543 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 0.870025543 + -0.5833333335 x = 0.870025543 + -0.5833333335 Combine like terms: 0.870025543 + -0.5833333335 = 0.2866922095 x = 0.2866922095 Simplifying x = 0.2866922095Subproblem 2
x + 0.5833333335 = -0.870025543 Simplifying x + 0.5833333335 = -0.870025543 Reorder the terms: 0.5833333335 + x = -0.870025543 Solving 0.5833333335 + x = -0.870025543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -0.870025543 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -0.870025543 + -0.5833333335 x = -0.870025543 + -0.5833333335 Combine like terms: -0.870025543 + -0.5833333335 = -1.4533588765 x = -1.4533588765 Simplifying x = -1.4533588765Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2866922095, -1.4533588765}
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