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Simplifying 9x(6x + -7) = -2 Reorder the terms: 9x(-7 + 6x) = -2 (-7 * 9x + 6x * 9x) = -2 (-63x + 54x2) = -2 Solving -63x + 54x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + -63x + 54x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -63x + 54x2 = 0 Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. 0.03703703704 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '-0.03703703704' to each side of the equation. 0.03703703704 + -1.166666667x + -0.03703703704 + x2 = 0 + -0.03703703704 Reorder the terms: 0.03703703704 + -0.03703703704 + -1.166666667x + x2 = 0 + -0.03703703704 Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000 0.00000000000 + -1.166666667x + x2 = 0 + -0.03703703704 -1.166666667x + x2 = 0 + -0.03703703704 Combine like terms: 0 + -0.03703703704 = -0.03703703704 -1.166666667x + x2 = -0.03703703704 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 = -0.03703703704 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = -0.03703703704 + 0.3402777780 Combine like terms: -0.03703703704 + 0.3402777780 = 0.30324074096 0.3402777780 + -1.166666667x + x2 = 0.30324074096 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.30324074096 Calculate the square root of the right side: 0.550672989 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.550672989 and -0.550672989.Subproblem 1
x + -0.5833333335 = 0.550672989 Simplifying x + -0.5833333335 = 0.550672989 Reorder the terms: -0.5833333335 + x = 0.550672989 Solving -0.5833333335 + x = 0.550672989 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 = 0.550672989 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.550672989 + 0.5833333335 x = 0.550672989 + 0.5833333335 Combine like terms: 0.550672989 + 0.5833333335 = 1.1340063225 x = 1.1340063225 Simplifying x = 1.1340063225Subproblem 2
x + -0.5833333335 = -0.550672989 Simplifying x + -0.5833333335 = -0.550672989 Reorder the terms: -0.5833333335 + x = -0.550672989 Solving -0.5833333335 + x = -0.550672989 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 = -0.550672989 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.550672989 + 0.5833333335 x = -0.550672989 + 0.5833333335 Combine like terms: -0.550672989 + 0.5833333335 = 0.0326603445 x = 0.0326603445 Simplifying x = 0.0326603445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1340063225, 0.0326603445}
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