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Simplifying (3x)(3x) + -3x + -5 = 0 Remove parenthesis around (3x) 3x(3x) + -3x + -5 = 0 Remove parenthesis around (3x) 3x * 3x + -3x + -5 = 0 Reorder the terms for easier multiplication: 3 * 3x * x + -3x + -5 = 0 Multiply 3 * 3 9x * x + -3x + -5 = 0 Multiply x * x 9x2 + -3x + -5 = 0 Reorder the terms: -5 + -3x + 9x2 = 0 Solving -5 + -3x + 9x2 = 0 Solving for variable 'x'. 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 = 0.9304292827 x = 0.9304292827 Simplifying x = 0.9304292827Subproblem 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 = -0.5970959493 x = -0.5970959493 Simplifying x = -0.5970959493Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9304292827, -0.5970959493}
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