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Simplifying 10a2 + -10 = 6a Reorder the terms: -10 + 10a2 = 6a Solving -10 + 10a2 = 6a Solving for variable 'a'. Reorder the terms: -10 + -6a + 10a2 = 6a + -6a Combine like terms: 6a + -6a = 0 -10 + -6a + 10a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -3a + 5a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -3a + 5a2)' equal to zero and attempt to solve: Simplifying -5 + -3a + 5a2 = 0 Solving -5 + -3a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -0.6a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.6a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + -0.6a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.6a + a2 = 0 + 1 -0.6a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.6a + a2 = 1 The a term is -0.6a. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6a + 0.09 + a2 = 1 + 0.09 Reorder the terms: 0.09 + -0.6a + a2 = 1 + 0.09 Combine like terms: 1 + 0.09 = 1.09 0.09 + -0.6a + a2 = 1.09 Factor a perfect square on the left side: (a + -0.3)(a + -0.3) = 1.09 Calculate the square root of the right side: 1.044030651 Break this problem into two subproblems by setting (a + -0.3) equal to 1.044030651 and -1.044030651.Subproblem 1
a + -0.3 = 1.044030651 Simplifying a + -0.3 = 1.044030651 Reorder the terms: -0.3 + a = 1.044030651 Solving -0.3 + a = 1.044030651 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + a = 1.044030651 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + a = 1.044030651 + 0.3 a = 1.044030651 + 0.3 Combine like terms: 1.044030651 + 0.3 = 1.344030651 a = 1.344030651 Simplifying a = 1.344030651Subproblem 2
a + -0.3 = -1.044030651 Simplifying a + -0.3 = -1.044030651 Reorder the terms: -0.3 + a = -1.044030651 Solving -0.3 + a = -1.044030651 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + a = -1.044030651 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + a = -1.044030651 + 0.3 a = -1.044030651 + 0.3 Combine like terms: -1.044030651 + 0.3 = -0.744030651 a = -0.744030651 Simplifying a = -0.744030651Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.344030651, -0.744030651}Solution
a = {1.344030651, -0.744030651}
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