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Simplifying 14x(6x + -7) = 79 Reorder the terms: 14x(-7 + 6x) = 79 (-7 * 14x + 6x * 14x) = 79 (-98x + 84x2) = 79 Solving -98x + 84x2 = 79 Solving for variable 'x'. Reorder the terms: -79 + -98x + 84x2 = 79 + -79 Combine like terms: 79 + -79 = 0 -79 + -98x + 84x2 = 0 Begin completing the square. Divide all terms by 84 the coefficient of the squared term: Divide each side by '84'. -0.9404761905 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '0.9404761905' to each side of the equation. -0.9404761905 + -1.166666667x + 0.9404761905 + x2 = 0 + 0.9404761905 Reorder the terms: -0.9404761905 + 0.9404761905 + -1.166666667x + x2 = 0 + 0.9404761905 Combine like terms: -0.9404761905 + 0.9404761905 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0 + 0.9404761905 -1.166666667x + x2 = 0 + 0.9404761905 Combine like terms: 0 + 0.9404761905 = 0.9404761905 -1.166666667x + x2 = 0.9404761905 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 = 0.9404761905 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 0.9404761905 + 0.3402777780 Combine like terms: 0.9404761905 + 0.3402777780 = 1.2807539685 0.3402777780 + -1.166666667x + x2 = 1.2807539685 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 1.2807539685 Calculate the square root of the right side: 1.131704011 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 1.131704011 and -1.131704011.Subproblem 1
x + -0.5833333335 = 1.131704011 Simplifying x + -0.5833333335 = 1.131704011 Reorder the terms: -0.5833333335 + x = 1.131704011 Solving -0.5833333335 + x = 1.131704011 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 = 1.131704011 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.131704011 + 0.5833333335 x = 1.131704011 + 0.5833333335 Combine like terms: 1.131704011 + 0.5833333335 = 1.7150373445 x = 1.7150373445 Simplifying x = 1.7150373445Subproblem 2
x + -0.5833333335 = -1.131704011 Simplifying x + -0.5833333335 = -1.131704011 Reorder the terms: -0.5833333335 + x = -1.131704011 Solving -0.5833333335 + x = -1.131704011 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 = -1.131704011 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.131704011 + 0.5833333335 x = -1.131704011 + 0.5833333335 Combine like terms: -1.131704011 + 0.5833333335 = -0.5483706775 x = -0.5483706775 Simplifying x = -0.5483706775Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7150373445, -0.5483706775}
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