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Simplifying 2x + -3(3x + 5) = 7x(3x + 1) Reorder the terms: 2x + -3(5 + 3x) = 7x(3x + 1) 2x + (5 * -3 + 3x * -3) = 7x(3x + 1) 2x + (-15 + -9x) = 7x(3x + 1) Reorder the terms: -15 + 2x + -9x = 7x(3x + 1) Combine like terms: 2x + -9x = -7x -15 + -7x = 7x(3x + 1) Reorder the terms: -15 + -7x = 7x(1 + 3x) -15 + -7x = (1 * 7x + 3x * 7x) -15 + -7x = (7x + 21x2) Solving -15 + -7x = 7x + 21x2 Solving for variable 'x'. Combine like terms: -7x + -7x = -14x -15 + -14x + -21x2 = 7x + 21x2 + -7x + -21x2 Reorder the terms: -15 + -14x + -21x2 = 7x + -7x + 21x2 + -21x2 Combine like terms: 7x + -7x = 0 -15 + -14x + -21x2 = 0 + 21x2 + -21x2 -15 + -14x + -21x2 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 -15 + -14x + -21x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 14x + 21x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 14x + 21x2)' equal to zero and attempt to solve: Simplifying 15 + 14x + 21x2 = 0 Solving 15 + 14x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.7142857143 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + 0.6666666667x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + 0.6666666667x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + -0.7142857143 0.6666666667x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 0.6666666667x + x2 = -0.7142857143 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -0.7142857143 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.7142857143 + 0.1111111112 Combine like terms: -0.7142857143 + 0.1111111112 = -0.6031746031 0.1111111112 + 0.6666666667x + x2 = -0.6031746031 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.6031746031 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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