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Simplifying 7x3(3x2 + -5x + 7) = 0 Reorder the terms: 7x3(7 + -5x + 3x2) = 0 (7 * 7x3 + -5x * 7x3 + 3x2 * 7x3) = 0 (49x3 + -35x4 + 21x5) = 0 Solving 49x3 + -35x4 + 21x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x3'. 7x3(7 + -5x + 3x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(7 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + -5x + 3x2 = 0 Solving 7 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -1.666666667x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -1.666666667x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + -2.333333333 -1.666666667x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -1.666666667x + x2 = -2.333333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -2.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -2.333333333 + 0.6944444447 Combine like terms: -2.333333333 + 0.6944444447 = -1.6388888883 0.6944444447 + -1.666666667x + x2 = -1.6388888883 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = -1.6388888883 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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