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Simplifying (3x + -3)(3x + 2) = 29 Reorder the terms: (-3 + 3x)(3x + 2) = 29 Reorder the terms: (-3 + 3x)(2 + 3x) = 29 Multiply (-3 + 3x) * (2 + 3x) (-3(2 + 3x) + 3x * (2 + 3x)) = 29 ((2 * -3 + 3x * -3) + 3x * (2 + 3x)) = 29 ((-6 + -9x) + 3x * (2 + 3x)) = 29 (-6 + -9x + (2 * 3x + 3x * 3x)) = 29 (-6 + -9x + (6x + 9x2)) = 29 Combine like terms: -9x + 6x = -3x (-6 + -3x + 9x2) = 29 Solving -6 + -3x + 9x2 = 29 Solving for variable 'x'. Reorder the terms: -6 + -29 + -3x + 9x2 = 29 + -29 Combine like terms: -6 + -29 = -35 -35 + -3x + 9x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -35 + -3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.888888889 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + -0.3333333333x + 3.888888889 + x2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + -0.3333333333x + x2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + -0.3333333333x + x2 = 0 + 3.888888889 -0.3333333333x + x2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 -0.3333333333x + x2 = 3.888888889 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 = 3.888888889 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 3.888888889 + 0.02777777779 Combine like terms: 3.888888889 + 0.02777777779 = 3.91666666679 0.02777777779 + -0.3333333333x + x2 = 3.91666666679 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 3.91666666679 Calculate the square root of the right side: 1.979057015 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 1.979057015 and -1.979057015.Subproblem 1
x + -0.1666666667 = 1.979057015 Simplifying x + -0.1666666667 = 1.979057015 Reorder the terms: -0.1666666667 + x = 1.979057015 Solving -0.1666666667 + x = 1.979057015 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 = 1.979057015 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.979057015 + 0.1666666667 x = 1.979057015 + 0.1666666667 Combine like terms: 1.979057015 + 0.1666666667 = 2.1457236817 x = 2.1457236817 Simplifying x = 2.1457236817Subproblem 2
x + -0.1666666667 = -1.979057015 Simplifying x + -0.1666666667 = -1.979057015 Reorder the terms: -0.1666666667 + x = -1.979057015 Solving -0.1666666667 + x = -1.979057015 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 = -1.979057015 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.979057015 + 0.1666666667 x = -1.979057015 + 0.1666666667 Combine like terms: -1.979057015 + 0.1666666667 = -1.8123903483 x = -1.8123903483 Simplifying x = -1.8123903483Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1457236817, -1.8123903483}
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