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Simplifying (3x + -2)(3x + -2) = 21 Reorder the terms: (-2 + 3x)(3x + -2) = 21 Reorder the terms: (-2 + 3x)(-2 + 3x) = 21 Multiply (-2 + 3x) * (-2 + 3x) (-2(-2 + 3x) + 3x * (-2 + 3x)) = 21 ((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = 21 ((4 + -6x) + 3x * (-2 + 3x)) = 21 (4 + -6x + (-2 * 3x + 3x * 3x)) = 21 (4 + -6x + (-6x + 9x2)) = 21 Combine like terms: -6x + -6x = -12x (4 + -12x + 9x2) = 21 Solving 4 + -12x + 9x2 = 21 Solving for variable 'x'. Reorder the terms: 4 + -21 + -12x + 9x2 = 21 + -21 Combine like terms: 4 + -21 = -17 -17 + -12x + 9x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -17 + -12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.888888889 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + -1.333333333x + 1.888888889 + x2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + -1.333333333x + x2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + 1.888888889 -1.333333333x + x2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 -1.333333333x + x2 = 1.888888889 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 1.888888889 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 1.888888889 + 0.4444444442 Combine like terms: 1.888888889 + 0.4444444442 = 2.3333333332 0.4444444442 + -1.333333333x + x2 = 2.3333333332 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 2.3333333332 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.527525232 and -1.527525232.Subproblem 1
x + -0.6666666665 = 1.527525232 Simplifying x + -0.6666666665 = 1.527525232 Reorder the terms: -0.6666666665 + x = 1.527525232 Solving -0.6666666665 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.527525232 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.527525232 + 0.6666666665 x = 1.527525232 + 0.6666666665 Combine like terms: 1.527525232 + 0.6666666665 = 2.1941918985 x = 2.1941918985 Simplifying x = 2.1941918985Subproblem 2
x + -0.6666666665 = -1.527525232 Simplifying x + -0.6666666665 = -1.527525232 Reorder the terms: -0.6666666665 + x = -1.527525232 Solving -0.6666666665 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.527525232 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.527525232 + 0.6666666665 x = -1.527525232 + 0.6666666665 Combine like terms: -1.527525232 + 0.6666666665 = -0.8608585655 x = -0.8608585655 Simplifying x = -0.8608585655Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1941918985, -0.8608585655}
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