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Simplifying -3x(x + 1) + -3x = -4x + 7 Reorder the terms: -3x(1 + x) + -3x = -4x + 7 (1 * -3x + x * -3x) + -3x = -4x + 7 (-3x + -3x2) + -3x = -4x + 7 Reorder the terms: -3x + -3x + -3x2 = -4x + 7 Combine like terms: -3x + -3x = -6x -6x + -3x2 = -4x + 7 Reorder the terms: -6x + -3x2 = 7 + -4x Solving -6x + -3x2 = 7 + -4x Solving for variable 'x'. Reorder the terms: -7 + -6x + 4x + -3x2 = 7 + -4x + -7 + 4x Combine like terms: -6x + 4x = -2x -7 + -2x + -3x2 = 7 + -4x + -7 + 4x Reorder the terms: -7 + -2x + -3x2 = 7 + -7 + -4x + 4x Combine like terms: 7 + -7 = 0 -7 + -2x + -3x2 = 0 + -4x + 4x -7 + -2x + -3x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -7 + -2x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 2x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + 2x + 3x2 = 0 Solving 7 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 0.6666666667x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 0.6666666667x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + -2.333333333 0.6666666667x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 0.6666666667x + x2 = -2.333333333 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 = -2.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -2.333333333 + 0.1111111112 Combine like terms: -2.333333333 + 0.1111111112 = -2.2222222218 0.1111111112 + 0.6666666667x + x2 = -2.2222222218 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -2.2222222218 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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