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Simplifying 3(x + 4) + -6x = 8 + -3(x + -5) * x Reorder the terms: 3(4 + x) + -6x = 8 + -3(x + -5) * x (4 * 3 + x * 3) + -6x = 8 + -3(x + -5) * x (12 + 3x) + -6x = 8 + -3(x + -5) * x Combine like terms: 3x + -6x = -3x 12 + -3x = 8 + -3(x + -5) * x Reorder the terms: 12 + -3x = 8 + -3(-5 + x) * x Reorder the terms for easier multiplication: 12 + -3x = 8 + -3x(-5 + x) 12 + -3x = 8 + (-5 * -3x + x * -3x) 12 + -3x = 8 + (15x + -3x2) Solving 12 + -3x = 8 + 15x + -3x2 Solving for variable 'x'. Reorder the terms: 12 + -8 + -3x + -15x + 3x2 = 8 + 15x + -3x2 + -8 + -15x + 3x2 Combine like terms: 12 + -8 = 4 4 + -3x + -15x + 3x2 = 8 + 15x + -3x2 + -8 + -15x + 3x2 Combine like terms: -3x + -15x = -18x 4 + -18x + 3x2 = 8 + 15x + -3x2 + -8 + -15x + 3x2 Reorder the terms: 4 + -18x + 3x2 = 8 + -8 + 15x + -15x + -3x2 + 3x2 Combine like terms: 8 + -8 = 0 4 + -18x + 3x2 = 0 + 15x + -15x + -3x2 + 3x2 4 + -18x + 3x2 = 15x + -15x + -3x2 + 3x2 Combine like terms: 15x + -15x = 0 4 + -18x + 3x2 = 0 + -3x2 + 3x2 4 + -18x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 4 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -6x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -6x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -6x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -6x + x2 = 0 + -1.333333333 -6x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -6x + x2 = -1.333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -1.333333333 + 9 Reorder the terms: 9 + -6x + x2 = -1.333333333 + 9 Combine like terms: -1.333333333 + 9 = 7.666666667 9 + -6x + x2 = 7.666666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 7.666666667 Calculate the square root of the right side: 2.768874621 Break this problem into two subproblems by setting (x + -3) equal to 2.768874621 and -2.768874621.Subproblem 1
x + -3 = 2.768874621 Simplifying x + -3 = 2.768874621 Reorder the terms: -3 + x = 2.768874621 Solving -3 + x = 2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.768874621 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.768874621 + 3 x = 2.768874621 + 3 Combine like terms: 2.768874621 + 3 = 5.768874621 x = 5.768874621 Simplifying x = 5.768874621Subproblem 2
x + -3 = -2.768874621 Simplifying x + -3 = -2.768874621 Reorder the terms: -3 + x = -2.768874621 Solving -3 + x = -2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.768874621 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.768874621 + 3 x = -2.768874621 + 3 Combine like terms: -2.768874621 + 3 = 0.231125379 x = 0.231125379 Simplifying x = 0.231125379Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.768874621, 0.231125379}
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