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Simplifying 50a2 + 75a2 + -8a + -12 = 0 Reorder the terms: -12 + -8a + 50a2 + 75a2 = 0 Combine like terms: 50a2 + 75a2 = 125a2 -12 + -8a + 125a2 = 0 Solving -12 + -8a + 125a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 125 the coefficient of the squared term: Divide each side by '125'. -0.096 + -0.064a + a2 = 0 Move the constant term to the right: Add '0.096' to each side of the equation. -0.096 + -0.064a + 0.096 + a2 = 0 + 0.096 Reorder the terms: -0.096 + 0.096 + -0.064a + a2 = 0 + 0.096 Combine like terms: -0.096 + 0.096 = 0.000 0.000 + -0.064a + a2 = 0 + 0.096 -0.064a + a2 = 0 + 0.096 Combine like terms: 0 + 0.096 = 0.096 -0.064a + a2 = 0.096 The a term is -0.064a. Take half its coefficient (-0.032). Square it (0.001024) and add it to both sides. Add '0.001024' to each side of the equation. -0.064a + 0.001024 + a2 = 0.096 + 0.001024 Reorder the terms: 0.001024 + -0.064a + a2 = 0.096 + 0.001024 Combine like terms: 0.096 + 0.001024 = 0.097024 0.001024 + -0.064a + a2 = 0.097024 Factor a perfect square on the left side: (a + -0.032)(a + -0.032) = 0.097024 Calculate the square root of the right side: 0.311486757 Break this problem into two subproblems by setting (a + -0.032) equal to 0.311486757 and -0.311486757.Subproblem 1
a + -0.032 = 0.311486757 Simplifying a + -0.032 = 0.311486757 Reorder the terms: -0.032 + a = 0.311486757 Solving -0.032 + a = 0.311486757 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.032' to each side of the equation. -0.032 + 0.032 + a = 0.311486757 + 0.032 Combine like terms: -0.032 + 0.032 = 0.000 0.000 + a = 0.311486757 + 0.032 a = 0.311486757 + 0.032 Combine like terms: 0.311486757 + 0.032 = 0.343486757 a = 0.343486757 Simplifying a = 0.343486757Subproblem 2
a + -0.032 = -0.311486757 Simplifying a + -0.032 = -0.311486757 Reorder the terms: -0.032 + a = -0.311486757 Solving -0.032 + a = -0.311486757 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.032' to each side of the equation. -0.032 + 0.032 + a = -0.311486757 + 0.032 Combine like terms: -0.032 + 0.032 = 0.000 0.000 + a = -0.311486757 + 0.032 a = -0.311486757 + 0.032 Combine like terms: -0.311486757 + 0.032 = -0.279486757 a = -0.279486757 Simplifying a = -0.279486757Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.343486757, -0.279486757}
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