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Simplifying -19 + -17x = (3x + 1)(x + -7) Reorder the terms: -19 + -17x = (1 + 3x)(x + -7) Reorder the terms: -19 + -17x = (1 + 3x)(-7 + x) Multiply (1 + 3x) * (-7 + x) -19 + -17x = (1(-7 + x) + 3x * (-7 + x)) -19 + -17x = ((-7 * 1 + x * 1) + 3x * (-7 + x)) -19 + -17x = ((-7 + 1x) + 3x * (-7 + x)) -19 + -17x = (-7 + 1x + (-7 * 3x + x * 3x)) -19 + -17x = (-7 + 1x + (-21x + 3x2)) Combine like terms: 1x + -21x = -20x -19 + -17x = (-7 + -20x + 3x2) Solving -19 + -17x = -7 + -20x + 3x2 Solving for variable 'x'. Reorder the terms: -19 + 7 + -17x + 20x + -3x2 = -7 + -20x + 3x2 + 7 + 20x + -3x2 Combine like terms: -19 + 7 = -12 -12 + -17x + 20x + -3x2 = -7 + -20x + 3x2 + 7 + 20x + -3x2 Combine like terms: -17x + 20x = 3x -12 + 3x + -3x2 = -7 + -20x + 3x2 + 7 + 20x + -3x2 Reorder the terms: -12 + 3x + -3x2 = -7 + 7 + -20x + 20x + 3x2 + -3x2 Combine like terms: -7 + 7 = 0 -12 + 3x + -3x2 = 0 + -20x + 20x + 3x2 + -3x2 -12 + 3x + -3x2 = -20x + 20x + 3x2 + -3x2 Combine like terms: -20x + 20x = 0 -12 + 3x + -3x2 = 0 + 3x2 + -3x2 -12 + 3x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -12 + 3x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + x + -1x2 = 0 Solving -4 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -1x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -1x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -1x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x + x2 = 0 + -4 -1x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1x + x2 = -4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + -1x + x2 = -3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.75 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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