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Simplifying 9x(3x + 1) = 15 Reorder the terms: 9x(1 + 3x) = 15 (1 * 9x + 3x * 9x) = 15 (9x + 27x2) = 15 Solving 9x + 27x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 9x + 27x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 9x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 3x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 3x + 9x2)' equal to zero and attempt to solve: Simplifying -5 + 3x + 9x2 = 0 Solving -5 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 0.3333333333x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 0.3333333333x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.5555555556 0.3333333333x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 0.3333333333x + x2 = 0.5555555556 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.5555555556 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.5555555556 + 0.02777777779 Combine like terms: 0.5555555556 + 0.02777777779 = 0.58333333339 0.02777777779 + 0.3333333333x + x2 = 0.58333333339 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.58333333339 Calculate the square root of the right side: 0.763762616 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.763762616 and -0.763762616.Subproblem 1
x + 0.1666666667 = 0.763762616 Simplifying x + 0.1666666667 = 0.763762616 Reorder the terms: 0.1666666667 + x = 0.763762616 Solving 0.1666666667 + x = 0.763762616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.763762616 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.763762616 + -0.1666666667 x = 0.763762616 + -0.1666666667 Combine like terms: 0.763762616 + -0.1666666667 = 0.5970959493 x = 0.5970959493 Simplifying x = 0.5970959493Subproblem 2
x + 0.1666666667 = -0.763762616 Simplifying x + 0.1666666667 = -0.763762616 Reorder the terms: 0.1666666667 + x = -0.763762616 Solving 0.1666666667 + x = -0.763762616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.763762616 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.763762616 + -0.1666666667 x = -0.763762616 + -0.1666666667 Combine like terms: -0.763762616 + -0.1666666667 = -0.9304292827 x = -0.9304292827 Simplifying x = -0.9304292827Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5970959493, -0.9304292827}Solution
x = {0.5970959493, -0.9304292827}
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