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Simplifying 3x(7x + -2) = -27 Reorder the terms: 3x(-2 + 7x) = -27 (-2 * 3x + 7x * 3x) = -27 (-6x + 21x2) = -27 Solving -6x + 21x2 = -27 Solving for variable 'x'. Reorder the terms: 27 + -6x + 21x2 = -27 + 27 Combine like terms: -27 + 27 = 0 27 + -6x + 21x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -2x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -2x + 7x2)' equal to zero and attempt to solve: Simplifying 9 + -2x + 7x2 = 0 Solving 9 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.285714286 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -0.2857142857x + -1.285714286 + x2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -0.2857142857x + x2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0 + -1.285714286 -0.2857142857x + x2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -0.2857142857x + x2 = -1.285714286 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = -1.285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = -1.285714286 + 0.02040816328 Combine like terms: -1.285714286 + 0.02040816328 = -1.26530612272 0.02040816328 + -0.2857142857x + x2 = -1.26530612272 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = -1.26530612272 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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