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Simplifying 7(a + -4) + -2a = 19 + 3a(a + 3) Reorder the terms: 7(-4 + a) + -2a = 19 + 3a(a + 3) (-4 * 7 + a * 7) + -2a = 19 + 3a(a + 3) (-28 + 7a) + -2a = 19 + 3a(a + 3) Combine like terms: 7a + -2a = 5a -28 + 5a = 19 + 3a(a + 3) Reorder the terms: -28 + 5a = 19 + 3a(3 + a) -28 + 5a = 19 + (3 * 3a + a * 3a) -28 + 5a = 19 + (9a + 3a2) Solving -28 + 5a = 19 + 9a + 3a2 Solving for variable 'a'. Reorder the terms: -28 + -19 + 5a + -9a + -3a2 = 19 + 9a + 3a2 + -19 + -9a + -3a2 Combine like terms: -28 + -19 = -47 -47 + 5a + -9a + -3a2 = 19 + 9a + 3a2 + -19 + -9a + -3a2 Combine like terms: 5a + -9a = -4a -47 + -4a + -3a2 = 19 + 9a + 3a2 + -19 + -9a + -3a2 Reorder the terms: -47 + -4a + -3a2 = 19 + -19 + 9a + -9a + 3a2 + -3a2 Combine like terms: 19 + -19 = 0 -47 + -4a + -3a2 = 0 + 9a + -9a + 3a2 + -3a2 -47 + -4a + -3a2 = 9a + -9a + 3a2 + -3a2 Combine like terms: 9a + -9a = 0 -47 + -4a + -3a2 = 0 + 3a2 + -3a2 -47 + -4a + -3a2 = 3a2 + -3a2 Combine like terms: 3a2 + -3a2 = 0 -47 + -4a + -3a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(47 + 4a + 3a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(47 + 4a + 3a2)' equal to zero and attempt to solve: Simplifying 47 + 4a + 3a2 = 0 Solving 47 + 4a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 15.66666667 + 1.333333333a + a2 = 0 Move the constant term to the right: Add '-15.66666667' to each side of the equation. 15.66666667 + 1.333333333a + -15.66666667 + a2 = 0 + -15.66666667 Reorder the terms: 15.66666667 + -15.66666667 + 1.333333333a + a2 = 0 + -15.66666667 Combine like terms: 15.66666667 + -15.66666667 = 0.00000000 0.00000000 + 1.333333333a + a2 = 0 + -15.66666667 1.333333333a + a2 = 0 + -15.66666667 Combine like terms: 0 + -15.66666667 = -15.66666667 1.333333333a + a2 = -15.66666667 The a term is 1.333333333a. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333a + 0.4444444442 + a2 = -15.66666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333a + a2 = -15.66666667 + 0.4444444442 Combine like terms: -15.66666667 + 0.4444444442 = -15.2222222258 0.4444444442 + 1.333333333a + a2 = -15.2222222258 Factor a perfect square on the left side: (a + 0.6666666665)(a + 0.6666666665) = -15.2222222258 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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