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Simplifying x(7 + -6x) = 0.95 (7 * x + -6x * x) = 0.95 (7x + -6x2) = 0.95 Solving 7x + -6x2 = 0.95 Solving for variable 'x'. Reorder the terms: -0.95 + 7x + -6x2 = 0.95 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 -0.95 + 7x + -6x2 = 0.00 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.1583333333 + -1.166666667x + x2 = 0.00 Move the constant term to the right: Add '-0.1583333333' to each side of the equation. 0.1583333333 + -1.166666667x + -0.1583333333 + x2 = 0.00 + -0.1583333333 Reorder the terms: 0.1583333333 + -0.1583333333 + -1.166666667x + x2 = 0.00 + -0.1583333333 Combine like terms: 0.1583333333 + -0.1583333333 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0.00 + -0.1583333333 -1.166666667x + x2 = 0.00 + -0.1583333333 Combine like terms: 0.00 + -0.1583333333 = -0.1583333333 -1.166666667x + x2 = -0.1583333333 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 = -0.1583333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = -0.1583333333 + 0.3402777780 Combine like terms: -0.1583333333 + 0.3402777780 = 0.1819444447 0.3402777780 + -1.166666667x + x2 = 0.1819444447 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.1819444447 Calculate the square root of the right side: 0.426549463 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.426549463 and -0.426549463.Subproblem 1
x + -0.5833333335 = 0.426549463 Simplifying x + -0.5833333335 = 0.426549463 Reorder the terms: -0.5833333335 + x = 0.426549463 Solving -0.5833333335 + x = 0.426549463 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 = 0.426549463 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.426549463 + 0.5833333335 x = 0.426549463 + 0.5833333335 Combine like terms: 0.426549463 + 0.5833333335 = 1.0098827965 x = 1.0098827965 Simplifying x = 1.0098827965Subproblem 2
x + -0.5833333335 = -0.426549463 Simplifying x + -0.5833333335 = -0.426549463 Reorder the terms: -0.5833333335 + x = -0.426549463 Solving -0.5833333335 + x = -0.426549463 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 = -0.426549463 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.426549463 + 0.5833333335 x = -0.426549463 + 0.5833333335 Combine like terms: -0.426549463 + 0.5833333335 = 0.1567838705 x = 0.1567838705 Simplifying x = 0.1567838705Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0098827965, 0.1567838705}
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