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Simplifying -84x2 + 98x + 196 = 0 Reorder the terms: 196 + 98x + -84x2 = 0 Solving 196 + 98x + -84x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '14'. 14(14 + 7x + -6x2) = 0 Ignore the factor 14.Subproblem 1
Set the factor '(14 + 7x + -6x2)' equal to zero and attempt to solve: Simplifying 14 + 7x + -6x2 = 0 Solving 14 + 7x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2.333333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -1.166666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -1.166666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 2.333333333 -1.166666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -1.166666667x + x2 = 2.333333333 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 = 2.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 2.333333333 + 0.3402777780 Combine like terms: 2.333333333 + 0.3402777780 = 2.673611111 0.3402777780 + -1.166666667x + x2 = 2.673611111 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 2.673611111 Calculate the square root of the right side: 1.635118072 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 1.635118072 and -1.635118072.Subproblem 1
x + -0.5833333335 = 1.635118072 Simplifying x + -0.5833333335 = 1.635118072 Reorder the terms: -0.5833333335 + x = 1.635118072 Solving -0.5833333335 + x = 1.635118072 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 = 1.635118072 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.635118072 + 0.5833333335 x = 1.635118072 + 0.5833333335 Combine like terms: 1.635118072 + 0.5833333335 = 2.2184514055 x = 2.2184514055 Simplifying x = 2.2184514055Subproblem 2
x + -0.5833333335 = -1.635118072 Simplifying x + -0.5833333335 = -1.635118072 Reorder the terms: -0.5833333335 + x = -1.635118072 Solving -0.5833333335 + x = -1.635118072 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 = -1.635118072 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.635118072 + 0.5833333335 x = -1.635118072 + 0.5833333335 Combine like terms: -1.635118072 + 0.5833333335 = -1.0517847385 x = -1.0517847385 Simplifying x = -1.0517847385Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2184514055, -1.0517847385}Solution
x = {2.2184514055, -1.0517847385}
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