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Simplifying (4 + 3x)(-3x) = -19 Remove parenthesis around (-3x) (4 + 3x) * -3x = -19 Reorder the terms for easier multiplication: -3x(4 + 3x) = -19 (4 * -3x + 3x * -3x) = -19 (-12x + -9x2) = -19 Solving -12x + -9x2 = -19 Solving for variable 'x'. Reorder the terms: 19 + -12x + -9x2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + -12x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.111111111 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '2.111111111' to each side of the equation. -2.111111111 + 1.333333333x + 2.111111111 + x2 = 0 + 2.111111111 Reorder the terms: -2.111111111 + 2.111111111 + 1.333333333x + x2 = 0 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + 2.111111111 1.333333333x + x2 = 0 + 2.111111111 Combine like terms: 0 + 2.111111111 = 2.111111111 1.333333333x + x2 = 2.111111111 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 = 2.111111111 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 2.111111111 + 0.4444444442 Combine like terms: 2.111111111 + 0.4444444442 = 2.5555555552 0.4444444442 + 1.333333333x + x2 = 2.5555555552 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 2.5555555552 Calculate the square root of the right side: 1.598610508 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.598610508 and -1.598610508.Subproblem 1
x + 0.6666666665 = 1.598610508 Simplifying x + 0.6666666665 = 1.598610508 Reorder the terms: 0.6666666665 + x = 1.598610508 Solving 0.6666666665 + x = 1.598610508 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 = 1.598610508 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.598610508 + -0.6666666665 x = 1.598610508 + -0.6666666665 Combine like terms: 1.598610508 + -0.6666666665 = 0.9319438415 x = 0.9319438415 Simplifying x = 0.9319438415Subproblem 2
x + 0.6666666665 = -1.598610508 Simplifying x + 0.6666666665 = -1.598610508 Reorder the terms: 0.6666666665 + x = -1.598610508 Solving 0.6666666665 + x = -1.598610508 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 = -1.598610508 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.598610508 + -0.6666666665 x = -1.598610508 + -0.6666666665 Combine like terms: -1.598610508 + -0.6666666665 = -2.2652771745 x = -2.2652771745 Simplifying x = -2.2652771745Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9319438415, -2.2652771745}
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