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Simplifying (2x + 1) + -2(x + -5) + 6 = 3x(x + 1) + (x + -1) + 23 Reorder the terms: (1 + 2x) + -2(x + -5) + 6 = 3x(x + 1) + (x + -1) + 23 Remove parenthesis around (1 + 2x) 1 + 2x + -2(x + -5) + 6 = 3x(x + 1) + (x + -1) + 23 Reorder the terms: 1 + 2x + -2(-5 + x) + 6 = 3x(x + 1) + (x + -1) + 23 1 + 2x + (-5 * -2 + x * -2) + 6 = 3x(x + 1) + (x + -1) + 23 1 + 2x + (10 + -2x) + 6 = 3x(x + 1) + (x + -1) + 23 Reorder the terms: 1 + 10 + 6 + 2x + -2x = 3x(x + 1) + (x + -1) + 23 Combine like terms: 1 + 10 = 11 11 + 6 + 2x + -2x = 3x(x + 1) + (x + -1) + 23 Combine like terms: 11 + 6 = 17 17 + 2x + -2x = 3x(x + 1) + (x + -1) + 23 Combine like terms: 2x + -2x = 0 17 + 0 = 3x(x + 1) + (x + -1) + 23 17 = 3x(x + 1) + (x + -1) + 23 Reorder the terms: 17 = 3x(1 + x) + (x + -1) + 23 17 = (1 * 3x + x * 3x) + (x + -1) + 23 17 = (3x + 3x2) + (x + -1) + 23 Reorder the terms: 17 = 3x + 3x2 + (-1 + x) + 23 Remove parenthesis around (-1 + x) 17 = 3x + 3x2 + -1 + x + 23 Reorder the terms: 17 = -1 + 23 + 3x + x + 3x2 Combine like terms: -1 + 23 = 22 17 = 22 + 3x + x + 3x2 Combine like terms: 3x + x = 4x 17 = 22 + 4x + 3x2 Solving 17 = 22 + 4x + 3x2 Solving for variable 'x'. Combine like terms: 17 + -22 = -5 -5 + -4x + -3x2 = 22 + 4x + 3x2 + -22 + -4x + -3x2 Reorder the terms: -5 + -4x + -3x2 = 22 + -22 + 4x + -4x + 3x2 + -3x2 Combine like terms: 22 + -22 = 0 -5 + -4x + -3x2 = 0 + 4x + -4x + 3x2 + -3x2 -5 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 -5 + -4x + -3x2 = 0 + 3x2 + -3x2 -5 + -4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -5 + -4x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 4x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + 4x + 3x2 = 0 Solving 5 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 1.333333333x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 1.333333333x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + -1.666666667 1.333333333x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 1.333333333x + x2 = -1.666666667 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 = -1.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -1.666666667 + 0.4444444442 Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228 0.4444444442 + 1.333333333x + x2 = -1.2222222228 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -1.2222222228 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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