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Simplifying (x + -3)(6x2 + x + -2) = 6 Reorder the terms: (-3 + x)(6x2 + x + -2) = 6 Reorder the terms: (-3 + x)(-2 + x + 6x2) = 6 Multiply (-3 + x) * (-2 + x + 6x2) (-3(-2 + x + 6x2) + x(-2 + x + 6x2)) = 6 ((-2 * -3 + x * -3 + 6x2 * -3) + x(-2 + x + 6x2)) = 6 ((6 + -3x + -18x2) + x(-2 + x + 6x2)) = 6 (6 + -3x + -18x2 + (-2 * x + x * x + 6x2 * x)) = 6 (6 + -3x + -18x2 + (-2x + x2 + 6x3)) = 6 Reorder the terms: (6 + -3x + -2x + -18x2 + x2 + 6x3) = 6 Combine like terms: -3x + -2x = -5x (6 + -5x + -18x2 + x2 + 6x3) = 6 Combine like terms: -18x2 + x2 = -17x2 (6 + -5x + -17x2 + 6x3) = 6 Add '-6' to each side of the equation. 6 + -5x + -17x2 + -6 + 6x3 = 6 + -6 Reorder the terms: 6 + -6 + -5x + -17x2 + 6x3 = 6 + -6 Combine like terms: 6 + -6 = 0 0 + -5x + -17x2 + 6x3 = 6 + -6 -5x + -17x2 + 6x3 = 6 + -6 Combine like terms: 6 + -6 = 0 -5x + -17x2 + 6x3 = 0 Solving -5x + -17x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + -17x + 6x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-5 + -17x + 6x2)' equal to zero and attempt to solve: Simplifying -5 + -17x + 6x2 = 0 Solving -5 + -17x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -2.833333333x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -2.833333333x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -2.833333333x + x2 = 0 + 0.8333333333 -2.833333333x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -2.833333333x + x2 = 0.8333333333 The x term is -2.833333333x. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333x + 2.006944445 + x2 = 0.8333333333 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = 0.8333333333 + 2.006944445 Combine like terms: 0.8333333333 + 2.006944445 = 2.8402777783 2.006944445 + -2.833333333x + x2 = 2.8402777783 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 2.8402777783 Calculate the square root of the right side: 1.685312368 Break this problem into two subproblems by setting (x + -1.416666667) equal to 1.685312368 and -1.685312368.Subproblem 1
x + -1.416666667 = 1.685312368 Simplifying x + -1.416666667 = 1.685312368 Reorder the terms: -1.416666667 + x = 1.685312368 Solving -1.416666667 + x = 1.685312368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = 1.685312368 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 1.685312368 + 1.416666667 x = 1.685312368 + 1.416666667 Combine like terms: 1.685312368 + 1.416666667 = 3.101979035 x = 3.101979035 Simplifying x = 3.101979035Subproblem 2
x + -1.416666667 = -1.685312368 Simplifying x + -1.416666667 = -1.685312368 Reorder the terms: -1.416666667 + x = -1.685312368 Solving -1.416666667 + x = -1.685312368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = -1.685312368 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -1.685312368 + 1.416666667 x = -1.685312368 + 1.416666667 Combine like terms: -1.685312368 + 1.416666667 = -0.268645701 x = -0.268645701 Simplifying x = -0.268645701Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.101979035, -0.268645701}Solution
x = {0, 3.101979035, -0.268645701}
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