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Simplifying -4((a * a) + 2) + 2((a * a) + 3) = 5a(a + -1) + 9 Multiply a * a -4((a2) + 2) + 2((a * a) + 3) = 5a(a + -1) + 9 -4(a2 + 2) + 2((a * a) + 3) = 5a(a + -1) + 9 Reorder the terms: -4(2 + a2) + 2((a * a) + 3) = 5a(a + -1) + 9 (2 * -4 + a2 * -4) + 2((a * a) + 3) = 5a(a + -1) + 9 (-8 + -4a2) + 2((a * a) + 3) = 5a(a + -1) + 9 Multiply a * a -8 + -4a2 + 2((a2) + 3) = 5a(a + -1) + 9 -8 + -4a2 + 2(a2 + 3) = 5a(a + -1) + 9 Reorder the terms: -8 + -4a2 + 2(3 + a2) = 5a(a + -1) + 9 -8 + -4a2 + (3 * 2 + a2 * 2) = 5a(a + -1) + 9 -8 + -4a2 + (6 + 2a2) = 5a(a + -1) + 9 Reorder the terms: -8 + 6 + -4a2 + 2a2 = 5a(a + -1) + 9 Combine like terms: -8 + 6 = -2 -2 + -4a2 + 2a2 = 5a(a + -1) + 9 Combine like terms: -4a2 + 2a2 = -2a2 -2 + -2a2 = 5a(a + -1) + 9 Reorder the terms: -2 + -2a2 = 5a(-1 + a) + 9 -2 + -2a2 = (-1 * 5a + a * 5a) + 9 -2 + -2a2 = (-5a + 5a2) + 9 Reorder the terms: -2 + -2a2 = 9 + -5a + 5a2 Solving -2 + -2a2 = 9 + -5a + 5a2 Solving for variable 'a'. Reorder the terms: -2 + -9 + 5a + -2a2 + -5a2 = 9 + -5a + 5a2 + -9 + 5a + -5a2 Combine like terms: -2 + -9 = -11 -11 + 5a + -2a2 + -5a2 = 9 + -5a + 5a2 + -9 + 5a + -5a2 Combine like terms: -2a2 + -5a2 = -7a2 -11 + 5a + -7a2 = 9 + -5a + 5a2 + -9 + 5a + -5a2 Reorder the terms: -11 + 5a + -7a2 = 9 + -9 + -5a + 5a + 5a2 + -5a2 Combine like terms: 9 + -9 = 0 -11 + 5a + -7a2 = 0 + -5a + 5a + 5a2 + -5a2 -11 + 5a + -7a2 = -5a + 5a + 5a2 + -5a2 Combine like terms: -5a + 5a = 0 -11 + 5a + -7a2 = 0 + 5a2 + -5a2 -11 + 5a + -7a2 = 5a2 + -5a2 Combine like terms: 5a2 + -5a2 = 0 -11 + 5a + -7a2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 1.571428571 + -0.7142857143a + a2 = 0 Move the constant term to the right: Add '-1.571428571' to each side of the equation. 1.571428571 + -0.7142857143a + -1.571428571 + a2 = 0 + -1.571428571 Reorder the terms: 1.571428571 + -1.571428571 + -0.7142857143a + a2 = 0 + -1.571428571 Combine like terms: 1.571428571 + -1.571428571 = 0.000000000 0.000000000 + -0.7142857143a + a2 = 0 + -1.571428571 -0.7142857143a + a2 = 0 + -1.571428571 Combine like terms: 0 + -1.571428571 = -1.571428571 -0.7142857143a + a2 = -1.571428571 The a term is -0.7142857143a. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143a + 0.1275510204 + a2 = -1.571428571 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143a + a2 = -1.571428571 + 0.1275510204 Combine like terms: -1.571428571 + 0.1275510204 = -1.4438775506 0.1275510204 + -0.7142857143a + a2 = -1.4438775506 Factor a perfect square on the left side: (a + -0.3571428572)(a + -0.3571428572) = -1.4438775506 Can't calculate square root of the right side. The solution to this equation could not be determined.
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