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Simplifying 6x(3x + 8) = 20 Reorder the terms: 6x(8 + 3x) = 20 (8 * 6x + 3x * 6x) = 20 (48x + 18x2) = 20 Solving 48x + 18x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 48x + 18x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 48x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 24x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 24x + 9x2)' equal to zero and attempt to solve: Simplifying -10 + 24x + 9x2 = 0 Solving -10 + 24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 2.666666667x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 2.666666667x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 2.666666667x + x2 = 0 + 1.111111111 2.666666667x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 2.666666667x + x2 = 1.111111111 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 1.111111111 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 1.111111111 + 1.777777780 Combine like terms: 1.111111111 + 1.777777780 = 2.888888891 1.777777780 + 2.666666667x + x2 = 2.888888891 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 2.888888891 Calculate the square root of the right side: 1.699673172 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.699673172 and -1.699673172.Subproblem 1
x + 1.333333334 = 1.699673172 Simplifying x + 1.333333334 = 1.699673172 Reorder the terms: 1.333333334 + x = 1.699673172 Solving 1.333333334 + x = 1.699673172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 1.699673172 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.699673172 + -1.333333334 x = 1.699673172 + -1.333333334 Combine like terms: 1.699673172 + -1.333333334 = 0.366339838 x = 0.366339838 Simplifying x = 0.366339838Subproblem 2
x + 1.333333334 = -1.699673172 Simplifying x + 1.333333334 = -1.699673172 Reorder the terms: 1.333333334 + x = -1.699673172 Solving 1.333333334 + x = -1.699673172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -1.699673172 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.699673172 + -1.333333334 x = -1.699673172 + -1.333333334 Combine like terms: -1.699673172 + -1.333333334 = -3.033006506 x = -3.033006506 Simplifying x = -3.033006506Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.366339838, -3.033006506}Solution
x = {0.366339838, -3.033006506}
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