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Simplifying (12x2) + -7x + -98 = 0 Reorder the terms: -98 + -7x + (12x2) = 0 Solving -98 + -7x + (12x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -8.166666667 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '8.166666667' to each side of the equation. -8.166666667 + -0.5833333333x + 8.166666667 + x2 = 0 + 8.166666667 Reorder the terms: -8.166666667 + 8.166666667 + -0.5833333333x + x2 = 0 + 8.166666667 Combine like terms: -8.166666667 + 8.166666667 = 0.000000000 0.000000000 + -0.5833333333x + x2 = 0 + 8.166666667 -0.5833333333x + x2 = 0 + 8.166666667 Combine like terms: 0 + 8.166666667 = 8.166666667 -0.5833333333x + x2 = 8.166666667 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 8.166666667 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 8.166666667 + 0.08506944446 Combine like terms: 8.166666667 + 0.08506944446 = 8.25173611146 0.08506944446 + -0.5833333333x + x2 = 8.25173611146 Factor a perfect square on the left side: ((x) + -0.2916666667)((x) + -0.2916666667) = 8.25173611146 Calculate the square root of the right side: 2.872583526 Break this problem into two subproblems by setting ((x) + -0.2916666667) equal to 2.872583526 and -2.872583526.Subproblem 1
(x) + -0.2916666667 = 2.872583526 Simplifying (x) + -0.2916666667 = 2.872583526 x + -0.2916666667 = 2.872583526 Reorder the terms: -0.2916666667 + x = 2.872583526 Solving -0.2916666667 + x = 2.872583526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 2.872583526 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 2.872583526 + 0.2916666667 x = 2.872583526 + 0.2916666667 Combine like terms: 2.872583526 + 0.2916666667 = 3.1642501927 x = 3.1642501927 Simplifying x = 3.1642501927Subproblem 2
(x) + -0.2916666667 = -2.872583526 Simplifying (x) + -0.2916666667 = -2.872583526 x + -0.2916666667 = -2.872583526 Reorder the terms: -0.2916666667 + x = -2.872583526 Solving -0.2916666667 + x = -2.872583526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -2.872583526 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -2.872583526 + 0.2916666667 x = -2.872583526 + 0.2916666667 Combine like terms: -2.872583526 + 0.2916666667 = -2.5809168593 x = -2.5809168593 Simplifying x = -2.5809168593Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1642501927, -2.5809168593}
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