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Simplifying 6x2 + 7x = 384 Reorder the terms: 7x + 6x2 = 384 Solving 7x + 6x2 = 384 Solving for variable 'x'. Reorder the terms: -384 + 7x + 6x2 = 384 + -384 Combine like terms: 384 + -384 = 0 -384 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -64 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 1.166666667x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 1.166666667x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 1.166666667x + x2 = 0 + 64 1.166666667x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 1.166666667x + x2 = 64 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 = 64 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 64 + 0.3402777780 Combine like terms: 64 + 0.3402777780 = 64.340277778 0.3402777780 + 1.166666667x + x2 = 64.340277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 64.340277778 Calculate the square root of the right side: 8.021239167 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 8.021239167 and -8.021239167.Subproblem 1
x + 0.5833333335 = 8.021239167 Simplifying x + 0.5833333335 = 8.021239167 Reorder the terms: 0.5833333335 + x = 8.021239167 Solving 0.5833333335 + x = 8.021239167 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 = 8.021239167 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 8.021239167 + -0.5833333335 x = 8.021239167 + -0.5833333335 Combine like terms: 8.021239167 + -0.5833333335 = 7.4379058335 x = 7.4379058335 Simplifying x = 7.4379058335Subproblem 2
x + 0.5833333335 = -8.021239167 Simplifying x + 0.5833333335 = -8.021239167 Reorder the terms: 0.5833333335 + x = -8.021239167 Solving 0.5833333335 + x = -8.021239167 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 = -8.021239167 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -8.021239167 + -0.5833333335 x = -8.021239167 + -0.5833333335 Combine like terms: -8.021239167 + -0.5833333335 = -8.6045725005 x = -8.6045725005 Simplifying x = -8.6045725005Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.4379058335, -8.6045725005}
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