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Simplifying 3x(20 + -7x) = 96 (20 * 3x + -7x * 3x) = 96 (60x + -21x2) = 96 Solving 60x + -21x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + 60x + -21x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 60x + -21x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-32 + 20x + -7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-32 + 20x + -7x2)' equal to zero and attempt to solve: Simplifying -32 + 20x + -7x2 = 0 Solving -32 + 20x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 4.571428571 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '-4.571428571' to each side of the equation. 4.571428571 + -2.857142857x + -4.571428571 + x2 = 0 + -4.571428571 Reorder the terms: 4.571428571 + -4.571428571 + -2.857142857x + x2 = 0 + -4.571428571 Combine like terms: 4.571428571 + -4.571428571 = 0.000000000 0.000000000 + -2.857142857x + x2 = 0 + -4.571428571 -2.857142857x + x2 = 0 + -4.571428571 Combine like terms: 0 + -4.571428571 = -4.571428571 -2.857142857x + x2 = -4.571428571 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = -4.571428571 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = -4.571428571 + 2.040816328 Combine like terms: -4.571428571 + 2.040816328 = -2.530612243 2.040816328 + -2.857142857x + x2 = -2.530612243 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = -2.530612243 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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