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Simplifying 4[3a * 3a + -4(a + -1)] = 0 Reorder the terms for easier multiplication: 4[3 * 3a * a + -4(a + -1)] = 0 Multiply 3 * 3 4[9a * a + -4(a + -1)] = 0 Multiply a * a 4[9a2 + -4(a + -1)] = 0 Reorder the terms: 4[9a2 + -4(-1 + a)] = 0 4[9a2 + (-1 * -4 + a * -4)] = 0 4[9a2 + (4 + -4a)] = 0 Reorder the terms: 4[4 + -4a + 9a2] = 0 [4 * 4 + -4a * 4 + 9a2 * 4] = 0 [16 + -16a + 36a2] = 0 Solving 16 + -16a + 36a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -4a + 9a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -4a + 9a2)' equal to zero and attempt to solve: Simplifying 4 + -4a + 9a2 = 0 Solving 4 + -4a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -0.4444444444a + a2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -0.4444444444a + -0.4444444444 + a2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -0.4444444444a + a2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -0.4444444444a + a2 = 0 + -0.4444444444 -0.4444444444a + a2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -0.4444444444a + a2 = -0.4444444444 The a term is -0.4444444444a. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444a + 0.04938271604 + a2 = -0.4444444444 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444a + a2 = -0.4444444444 + 0.04938271604 Combine like terms: -0.4444444444 + 0.04938271604 = -0.39506172836 0.04938271604 + -0.4444444444a + a2 = -0.39506172836 Factor a perfect square on the left side: (a + -0.2222222222)(a + -0.2222222222) = -0.39506172836 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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