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Simplifying 6x2 + -7x = 216 Reorder the terms: -7x + 6x2 = 216 Solving -7x + 6x2 = 216 Solving for variable 'x'. Reorder the terms: -216 + -7x + 6x2 = 216 + -216 Combine like terms: 216 + -216 = 0 -216 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -36 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -1.166666667x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -1.166666667x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1.166666667x + x2 = 0 + 36 -1.166666667x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1.166666667x + x2 = 36 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 = 36 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 36 + 0.3402777780 Combine like terms: 36 + 0.3402777780 = 36.340277778 0.3402777780 + -1.166666667x + x2 = 36.340277778 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 36.340277778 Calculate the square root of the right side: 6.028289789 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 6.028289789 and -6.028289789.Subproblem 1
x + -0.5833333335 = 6.028289789 Simplifying x + -0.5833333335 = 6.028289789 Reorder the terms: -0.5833333335 + x = 6.028289789 Solving -0.5833333335 + x = 6.028289789 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 = 6.028289789 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 6.028289789 + 0.5833333335 x = 6.028289789 + 0.5833333335 Combine like terms: 6.028289789 + 0.5833333335 = 6.6116231225 x = 6.6116231225 Simplifying x = 6.6116231225Subproblem 2
x + -0.5833333335 = -6.028289789 Simplifying x + -0.5833333335 = -6.028289789 Reorder the terms: -0.5833333335 + x = -6.028289789 Solving -0.5833333335 + x = -6.028289789 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 = -6.028289789 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -6.028289789 + 0.5833333335 x = -6.028289789 + 0.5833333335 Combine like terms: -6.028289789 + 0.5833333335 = -5.4449564555 x = -5.4449564555 Simplifying x = -5.4449564555Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6116231225, -5.4449564555}
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