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Simplifying 5a2 + -12a = 4 Reorder the terms: -12a + 5a2 = 4 Solving -12a + 5a2 = 4 Solving for variable 'a'. Reorder the terms: -4 + -12a + 5a2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -12a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -2.4a + a2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -2.4a + 0.8 + a2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -2.4a + a2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -2.4a + a2 = 0 + 0.8 -2.4a + a2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -2.4a + a2 = 0.8 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 = 0.8 + 1.44 Reorder the terms: 1.44 + -2.4a + a2 = 0.8 + 1.44 Combine like terms: 0.8 + 1.44 = 2.24 1.44 + -2.4a + a2 = 2.24 Factor a perfect square on the left side: (a + -1.2)(a + -1.2) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (a + -1.2) equal to 1.496662955 and -1.496662955.Subproblem 1
a + -1.2 = 1.496662955 Simplifying a + -1.2 = 1.496662955 Reorder the terms: -1.2 + a = 1.496662955 Solving -1.2 + a = 1.496662955 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 = 1.496662955 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + a = 1.496662955 + 1.2 a = 1.496662955 + 1.2 Combine like terms: 1.496662955 + 1.2 = 2.696662955 a = 2.696662955 Simplifying a = 2.696662955Subproblem 2
a + -1.2 = -1.496662955 Simplifying a + -1.2 = -1.496662955 Reorder the terms: -1.2 + a = -1.496662955 Solving -1.2 + a = -1.496662955 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 = -1.496662955 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + a = -1.496662955 + 1.2 a = -1.496662955 + 1.2 Combine like terms: -1.496662955 + 1.2 = -0.296662955 a = -0.296662955 Simplifying a = -0.296662955Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.696662955, -0.296662955}
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