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Simplifying (x + 8)(6x + 2) + -10 = 0 Reorder the terms: (8 + x)(6x + 2) + -10 = 0 Reorder the terms: (8 + x)(2 + 6x) + -10 = 0 Multiply (8 + x) * (2 + 6x) (8(2 + 6x) + x(2 + 6x)) + -10 = 0 ((2 * 8 + 6x * 8) + x(2 + 6x)) + -10 = 0 ((16 + 48x) + x(2 + 6x)) + -10 = 0 (16 + 48x + (2 * x + 6x * x)) + -10 = 0 (16 + 48x + (2x + 6x2)) + -10 = 0 Combine like terms: 48x + 2x = 50x (16 + 50x + 6x2) + -10 = 0 Reorder the terms: 16 + -10 + 50x + 6x2 = 0 Combine like terms: 16 + -10 = 6 6 + 50x + 6x2 = 0 Solving 6 + 50x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 25x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 25x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + 25x + 3x2 = 0 Solving 3 + 25x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 8.333333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 8.333333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 8.333333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8.333333333x + x2 = 0 + -1 8.333333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 8.333333333x + x2 = -1 The x term is 8.333333333x. Take half its coefficient (4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. 8.333333333x + 17.36111111 + x2 = -1 + 17.36111111 Reorder the terms: 17.36111111 + 8.333333333x + x2 = -1 + 17.36111111 Combine like terms: -1 + 17.36111111 = 16.36111111 17.36111111 + 8.333333333x + x2 = 16.36111111 Factor a perfect square on the left side: (x + 4.166666667)(x + 4.166666667) = 16.36111111 Calculate the square root of the right side: 4.044887033 Break this problem into two subproblems by setting (x + 4.166666667) equal to 4.044887033 and -4.044887033.Subproblem 1
x + 4.166666667 = 4.044887033 Simplifying x + 4.166666667 = 4.044887033 Reorder the terms: 4.166666667 + x = 4.044887033 Solving 4.166666667 + x = 4.044887033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 4.044887033 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 4.044887033 + -4.166666667 x = 4.044887033 + -4.166666667 Combine like terms: 4.044887033 + -4.166666667 = -0.121779634 x = -0.121779634 Simplifying x = -0.121779634Subproblem 2
x + 4.166666667 = -4.044887033 Simplifying x + 4.166666667 = -4.044887033 Reorder the terms: 4.166666667 + x = -4.044887033 Solving 4.166666667 + x = -4.044887033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -4.044887033 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -4.044887033 + -4.166666667 x = -4.044887033 + -4.166666667 Combine like terms: -4.044887033 + -4.166666667 = -8.2115537 x = -8.2115537 Simplifying x = -8.2115537Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.121779634, -8.2115537}Solution
x = {-0.121779634, -8.2115537}
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