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Simplifying 2x2(3a2 + -2a + 3) = 0 Reorder the terms: 2x2(3 + -2a + 3a2) = 0 (3 * 2x2 + -2a * 2x2 + 3a2 * 2x2) = 0 Reorder the terms: (-4ax2 + 6a2x2 + 6x2) = 0 (-4ax2 + 6a2x2 + 6x2) = 0 Solving -4ax2 + 6a2x2 + 6x2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-2a + 3a2 + 3) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 = 0 + -1x2 Remove the zero: 0 = -1x2 Simplifying 0 = -1x2 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 '(-2a + 3a2 + 3)' equal to zero and attempt to solve: Simplifying -2a + 3a2 + 3 = 0 Reorder the terms: 3 + -2a + 3a2 = 0 Solving 3 + -2a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -0.6666666667a + a2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.6666666667a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + -0.6666666667a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.6666666667a + a2 = 0 + -1 -0.6666666667a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.6666666667a + a2 = -1 The a term is -0.6666666667a. 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. -0.6666666667a + 0.1111111112 + a2 = -1 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667a + a2 = -1 + 0.1111111112 Combine like terms: -1 + 0.1111111112 = -0.8888888888 0.1111111112 + -0.6666666667a + a2 = -0.8888888888 Factor a perfect square on the left side: (a + -0.3333333334)(a + -0.3333333334) = -0.8888888888 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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