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Simplifying 0 = -6x2 + 7x + 4 Reorder the terms: 0 = 4 + 7x + -6x2 Solving 0 = 4 + 7x + -6x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -7x + 6x2 = 4 + 7x + -6x2 + -4 + -7x + 6x2 Reorder the terms: -4 + -7x + 6x2 = 4 + -4 + 7x + -7x + -6x2 + 6x2 Combine like terms: 4 + -4 = 0 -4 + -7x + 6x2 = 0 + 7x + -7x + -6x2 + 6x2 -4 + -7x + 6x2 = 7x + -7x + -6x2 + 6x2 Combine like terms: 7x + -7x = 0 -4 + -7x + 6x2 = 0 + -6x2 + 6x2 -4 + -7x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -4 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.6666666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1.166666667x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1.166666667x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0 + 0.6666666667 -1.166666667x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1.166666667x + x2 = 0.6666666667 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 = 0.6666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 0.6666666667 + 0.3402777780 Combine like terms: 0.6666666667 + 0.3402777780 = 1.0069444447 0.3402777780 + -1.166666667x + x2 = 1.0069444447 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 1.0069444447 Calculate the square root of the right side: 1.003466215 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 1.003466215 and -1.003466215.Subproblem 1
x + -0.5833333335 = 1.003466215 Simplifying x + -0.5833333335 = 1.003466215 Reorder the terms: -0.5833333335 + x = 1.003466215 Solving -0.5833333335 + x = 1.003466215 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 = 1.003466215 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.003466215 + 0.5833333335 x = 1.003466215 + 0.5833333335 Combine like terms: 1.003466215 + 0.5833333335 = 1.5867995485 x = 1.5867995485 Simplifying x = 1.5867995485Subproblem 2
x + -0.5833333335 = -1.003466215 Simplifying x + -0.5833333335 = -1.003466215 Reorder the terms: -0.5833333335 + x = -1.003466215 Solving -0.5833333335 + x = -1.003466215 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 = -1.003466215 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.003466215 + 0.5833333335 x = -1.003466215 + 0.5833333335 Combine like terms: -1.003466215 + 0.5833333335 = -0.4201328815 x = -0.4201328815 Simplifying x = -0.4201328815Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5867995485, -0.4201328815}
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