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Simplifying 4x3(6x2 + -4x + 7) = 0 Reorder the terms: 4x3(7 + -4x + 6x2) = 0 (7 * 4x3 + -4x * 4x3 + 6x2 * 4x3) = 0 (28x3 + -16x4 + 24x5) = 0 Solving 28x3 + -16x4 + 24x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x3'. 4x3(7 + -4x + 6x2) = 0 Ignore the factor 4.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 + -4x + 6x2)' equal to zero and attempt to solve: Simplifying 7 + -4x + 6x2 = 0 Solving 7 + -4x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + -0.6666666667x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + -0.6666666667x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + -1.166666667 -0.6666666667x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 -0.6666666667x + x2 = -1.166666667 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 = -1.166666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -1.166666667 + 0.1111111112 Combine like terms: -1.166666667 + 0.1111111112 = -1.0555555558 0.1111111112 + -0.6666666667x + x2 = -1.0555555558 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -1.0555555558 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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