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Simplifying 6x2 + -7x + -54 = 0 Reorder the terms: -54 + -7x + 6x2 = 0 Solving -54 + -7x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -9 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -1.166666667x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -1.166666667x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1.166666667x + x2 = 0 + 9 -1.166666667x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1.166666667x + x2 = 9 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 = 9 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 9 + 0.3402777780 Combine like terms: 9 + 0.3402777780 = 9.340277778 0.3402777780 + -1.166666667x + x2 = 9.340277778 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 9.340277778 Calculate the square root of the right side: 3.056186804 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 3.056186804 and -3.056186804.Subproblem 1
x + -0.5833333335 = 3.056186804 Simplifying x + -0.5833333335 = 3.056186804 Reorder the terms: -0.5833333335 + x = 3.056186804 Solving -0.5833333335 + x = 3.056186804 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 = 3.056186804 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 3.056186804 + 0.5833333335 x = 3.056186804 + 0.5833333335 Combine like terms: 3.056186804 + 0.5833333335 = 3.6395201375 x = 3.6395201375 Simplifying x = 3.6395201375Subproblem 2
x + -0.5833333335 = -3.056186804 Simplifying x + -0.5833333335 = -3.056186804 Reorder the terms: -0.5833333335 + x = -3.056186804 Solving -0.5833333335 + x = -3.056186804 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 = -3.056186804 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -3.056186804 + 0.5833333335 x = -3.056186804 + 0.5833333335 Combine like terms: -3.056186804 + 0.5833333335 = -2.4728534705 x = -2.4728534705 Simplifying x = -2.4728534705Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6395201375, -2.4728534705}
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