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Simplifying 15a2 = 36a + 30 Reorder the terms: 15a2 = 30 + 36a Solving 15a2 = 30 + 36a Solving for variable 'a'. Reorder the terms: -30 + -36a + 15a2 = 30 + 36a + -30 + -36a Reorder the terms: -30 + -36a + 15a2 = 30 + -30 + 36a + -36a Combine like terms: 30 + -30 = 0 -30 + -36a + 15a2 = 0 + 36a + -36a -30 + -36a + 15a2 = 36a + -36a Combine like terms: 36a + -36a = 0 -30 + -36a + 15a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -12a + 5a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + -12a + 5a2)' equal to zero and attempt to solve: Simplifying -10 + -12a + 5a2 = 0 Solving -10 + -12a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -2.4a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.4a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -2.4a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.4a + a2 = 0 + 2 -2.4a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.4a + a2 = 2 The a term is -2.4a. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4a + 1.44 + a2 = 2 + 1.44 Reorder the terms: 1.44 + -2.4a + a2 = 2 + 1.44 Combine like terms: 2 + 1.44 = 3.44 1.44 + -2.4a + a2 = 3.44 Factor a perfect square on the left side: (a + -1.2)(a + -1.2) = 3.44 Calculate the square root of the right side: 1.854723699 Break this problem into two subproblems by setting (a + -1.2) equal to 1.854723699 and -1.854723699.Subproblem 1
a + -1.2 = 1.854723699 Simplifying a + -1.2 = 1.854723699 Reorder the terms: -1.2 + a = 1.854723699 Solving -1.2 + a = 1.854723699 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + a = 1.854723699 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + a = 1.854723699 + 1.2 a = 1.854723699 + 1.2 Combine like terms: 1.854723699 + 1.2 = 3.054723699 a = 3.054723699 Simplifying a = 3.054723699Subproblem 2
a + -1.2 = -1.854723699 Simplifying a + -1.2 = -1.854723699 Reorder the terms: -1.2 + a = -1.854723699 Solving -1.2 + a = -1.854723699 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + a = -1.854723699 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + a = -1.854723699 + 1.2 a = -1.854723699 + 1.2 Combine like terms: -1.854723699 + 1.2 = -0.654723699 a = -0.654723699 Simplifying a = -0.654723699Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.054723699, -0.654723699}Solution
a = {3.054723699, -0.654723699}
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