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Simplifying -21x + 12 + -18x2 = 0 Reorder the terms: 12 + -21x + -18x2 = 0 Solving 12 + -21x + -18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -7x + -6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -7x + -6x2)' equal to zero and attempt to solve: Simplifying 4 + -7x + -6x2 = 0 Solving 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 = 0.4201328815 x = 0.4201328815 Simplifying x = 0.4201328815Subproblem 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 = -1.5867995485 x = -1.5867995485 Simplifying x = -1.5867995485Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4201328815, -1.5867995485}Solution
x = {0.4201328815, -1.5867995485}
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