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Simplifying (12a2 + -7a + 5) + -1(-8a2 + a + 9) = 0 Reorder the terms: (5 + -7a + 12a2) + -1(-8a2 + a + 9) = 0 Remove parenthesis around (5 + -7a + 12a2) 5 + -7a + 12a2 + -1(-8a2 + a + 9) = 0 Reorder the terms: 5 + -7a + 12a2 + -1(9 + a + -8a2) = 0 5 + -7a + 12a2 + (9 * -1 + a * -1 + -8a2 * -1) = 0 5 + -7a + 12a2 + (-9 + -1a + 8a2) = 0 Reorder the terms: 5 + -9 + -7a + -1a + 12a2 + 8a2 = 0 Combine like terms: 5 + -9 = -4 -4 + -7a + -1a + 12a2 + 8a2 = 0 Combine like terms: -7a + -1a = -8a -4 + -8a + 12a2 + 8a2 = 0 Combine like terms: 12a2 + 8a2 = 20a2 -4 + -8a + 20a2 = 0 Solving -4 + -8a + 20a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -2a + 5a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -2a + 5a2)' equal to zero and attempt to solve: Simplifying -1 + -2a + 5a2 = 0 Solving -1 + -2a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -0.4a + a2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.4a + 0.2 + a2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.4a + a2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.4a + a2 = 0 + 0.2 -0.4a + a2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.4a + a2 = 0.2 The a term is -0.4a. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4a + 0.04 + a2 = 0.2 + 0.04 Reorder the terms: 0.04 + -0.4a + a2 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + -0.4a + a2 = 0.24 Factor a perfect square on the left side: (a + -0.2)(a + -0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (a + -0.2) equal to 0.489897949 and -0.489897949.Subproblem 1
a + -0.2 = 0.489897949 Simplifying a + -0.2 = 0.489897949 Reorder the terms: -0.2 + a = 0.489897949 Solving -0.2 + a = 0.489897949 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + a = 0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + a = 0.489897949 + 0.2 a = 0.489897949 + 0.2 Combine like terms: 0.489897949 + 0.2 = 0.689897949 a = 0.689897949 Simplifying a = 0.689897949Subproblem 2
a + -0.2 = -0.489897949 Simplifying a + -0.2 = -0.489897949 Reorder the terms: -0.2 + a = -0.489897949 Solving -0.2 + a = -0.489897949 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + a = -0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + a = -0.489897949 + 0.2 a = -0.489897949 + 0.2 Combine like terms: -0.489897949 + 0.2 = -0.289897949 a = -0.289897949 Simplifying a = -0.289897949Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.689897949, -0.289897949}Solution
a = {0.689897949, -0.289897949}
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