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Simplifying 19a + -1(-12) + -5a2 = 0 Multiply -1 * -12 19a + 12 + -5a2 = 0 Reorder the terms: 12 + 19a + -5a2 = 0 Solving 12 + 19a + -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'. -2.4 + -3.8a + a2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -3.8a + 2.4 + a2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -3.8a + a2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -3.8a + a2 = 0 + 2.4 -3.8a + a2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -3.8a + a2 = 2.4 The a term is -3.8a. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8a + 3.61 + a2 = 2.4 + 3.61 Reorder the terms: 3.61 + -3.8a + a2 = 2.4 + 3.61 Combine like terms: 2.4 + 3.61 = 6.01 3.61 + -3.8a + a2 = 6.01 Factor a perfect square on the left side: (a + -1.9)(a + -1.9) = 6.01 Calculate the square root of the right side: 2.451530134 Break this problem into two subproblems by setting (a + -1.9) equal to 2.451530134 and -2.451530134.Subproblem 1
a + -1.9 = 2.451530134 Simplifying a + -1.9 = 2.451530134 Reorder the terms: -1.9 + a = 2.451530134 Solving -1.9 + a = 2.451530134 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + a = 2.451530134 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + a = 2.451530134 + 1.9 a = 2.451530134 + 1.9 Combine like terms: 2.451530134 + 1.9 = 4.351530134 a = 4.351530134 Simplifying a = 4.351530134Subproblem 2
a + -1.9 = -2.451530134 Simplifying a + -1.9 = -2.451530134 Reorder the terms: -1.9 + a = -2.451530134 Solving -1.9 + a = -2.451530134 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + a = -2.451530134 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + a = -2.451530134 + 1.9 a = -2.451530134 + 1.9 Combine like terms: -2.451530134 + 1.9 = -0.551530134 a = -0.551530134 Simplifying a = -0.551530134Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.351530134, -0.551530134}
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