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Simplifying 6x + (3x + -1) = 6x(3x + -1) Reorder the terms: 6x + (-1 + 3x) = 6x(3x + -1) Remove parenthesis around (-1 + 3x) 6x + -1 + 3x = 6x(3x + -1) Reorder the terms: -1 + 6x + 3x = 6x(3x + -1) Combine like terms: 6x + 3x = 9x -1 + 9x = 6x(3x + -1) Reorder the terms: -1 + 9x = 6x(-1 + 3x) -1 + 9x = (-1 * 6x + 3x * 6x) -1 + 9x = (-6x + 18x2) Solving -1 + 9x = -6x + 18x2 Solving for variable 'x'. Combine like terms: 9x + 6x = 15x -1 + 15x + -18x2 = -6x + 18x2 + 6x + -18x2 Reorder the terms: -1 + 15x + -18x2 = -6x + 6x + 18x2 + -18x2 Combine like terms: -6x + 6x = 0 -1 + 15x + -18x2 = 0 + 18x2 + -18x2 -1 + 15x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -1 + 15x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. 0.05555555556 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + -0.8333333333x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + -0.8333333333x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + -0.8333333333x + x2 = 0 + -0.05555555556 -0.8333333333x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 -0.8333333333x + x2 = -0.05555555556 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = -0.05555555556 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = -0.05555555556 + 0.1736111111 Combine like terms: -0.05555555556 + 0.1736111111 = 0.11805555554 0.1736111111 + -0.8333333333x + x2 = 0.11805555554 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 0.11805555554 Calculate the square root of the right side: 0.343592135 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 0.343592135 and -0.343592135.Subproblem 1
x + -0.4166666667 = 0.343592135 Simplifying x + -0.4166666667 = 0.343592135 Reorder the terms: -0.4166666667 + x = 0.343592135 Solving -0.4166666667 + x = 0.343592135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 0.343592135 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 0.343592135 + 0.4166666667 x = 0.343592135 + 0.4166666667 Combine like terms: 0.343592135 + 0.4166666667 = 0.7602588017 x = 0.7602588017 Simplifying x = 0.7602588017Subproblem 2
x + -0.4166666667 = -0.343592135 Simplifying x + -0.4166666667 = -0.343592135 Reorder the terms: -0.4166666667 + x = -0.343592135 Solving -0.4166666667 + x = -0.343592135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -0.343592135 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -0.343592135 + 0.4166666667 x = -0.343592135 + 0.4166666667 Combine like terms: -0.343592135 + 0.4166666667 = 0.0730745317 x = 0.0730745317 Simplifying x = 0.0730745317Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7602588017, 0.0730745317}
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