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Simplifying (7a2 + -9a + 6) + -1(12a2 + -4a + 3) = 0 Reorder the terms: (6 + -9a + 7a2) + -1(12a2 + -4a + 3) = 0 Remove parenthesis around (6 + -9a + 7a2) 6 + -9a + 7a2 + -1(12a2 + -4a + 3) = 0 Reorder the terms: 6 + -9a + 7a2 + -1(3 + -4a + 12a2) = 0 6 + -9a + 7a2 + (3 * -1 + -4a * -1 + 12a2 * -1) = 0 6 + -9a + 7a2 + (-3 + 4a + -12a2) = 0 Reorder the terms: 6 + -3 + -9a + 4a + 7a2 + -12a2 = 0 Combine like terms: 6 + -3 = 3 3 + -9a + 4a + 7a2 + -12a2 = 0 Combine like terms: -9a + 4a = -5a 3 + -5a + 7a2 + -12a2 = 0 Combine like terms: 7a2 + -12a2 = -5a2 3 + -5a + -5a2 = 0 Solving 3 + -5a + -5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + a + a2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + a + 0.6 + a2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + a + a2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + a + a2 = 0 + 0.6 a + a2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 a + a2 = 0.6 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = 0.6 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 0.6 + 0.25 Combine like terms: 0.6 + 0.25 = 0.85 1.25 + a2 = 0.85 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 0.85 Calculate the square root of the right side: 0.921954446 Break this problem into two subproblems by setting (a + 0.5) equal to 0.921954446 and -0.921954446.Subproblem 1
a + 0.5 = 0.921954446 Simplifying a + 0.5 = 0.921954446 Reorder the terms: 0.5 + a = 0.921954446 Solving 0.5 + a = 0.921954446 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 0.921954446 + -0.5 a = 0.921954446 + -0.5 Combine like terms: 0.921954446 + -0.5 = 0.421954446 a = 0.421954446 Simplifying a = 0.421954446Subproblem 2
a + 0.5 = -0.921954446 Simplifying a + 0.5 = -0.921954446 Reorder the terms: 0.5 + a = -0.921954446 Solving 0.5 + a = -0.921954446 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -0.921954446 + -0.5 a = -0.921954446 + -0.5 Combine like terms: -0.921954446 + -0.5 = -1.421954446 a = -1.421954446 Simplifying a = -1.421954446Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.421954446, -1.421954446}
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