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Simplifying 4a2 + -7 = a Reorder the terms: -7 + 4a2 = a Solving -7 + 4a2 = a Solving for variable 'a'. Reorder the terms: -7 + -1a + 4a2 = a + -1a Combine like terms: a + -1a = 0 -7 + -1a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -0.25a + a2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -0.25a + 1.75 + a2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -0.25a + a2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -0.25a + a2 = 0 + 1.75 -0.25a + a2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -0.25a + a2 = 1.75 The a term is -0.25a. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25a + 0.015625 + a2 = 1.75 + 0.015625 Reorder the terms: 0.015625 + -0.25a + a2 = 1.75 + 0.015625 Combine like terms: 1.75 + 0.015625 = 1.765625 0.015625 + -0.25a + a2 = 1.765625 Factor a perfect square on the left side: (a + -0.125)(a + -0.125) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (a + -0.125) equal to 1.328768227 and -1.328768227.Subproblem 1
a + -0.125 = 1.328768227 Simplifying a + -0.125 = 1.328768227 Reorder the terms: -0.125 + a = 1.328768227 Solving -0.125 + a = 1.328768227 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = 1.328768227 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = 1.328768227 + 0.125 a = 1.328768227 + 0.125 Combine like terms: 1.328768227 + 0.125 = 1.453768227 a = 1.453768227 Simplifying a = 1.453768227Subproblem 2
a + -0.125 = -1.328768227 Simplifying a + -0.125 = -1.328768227 Reorder the terms: -0.125 + a = -1.328768227 Solving -0.125 + a = -1.328768227 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = -1.328768227 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = -1.328768227 + 0.125 a = -1.328768227 + 0.125 Combine like terms: -1.328768227 + 0.125 = -1.203768227 a = -1.203768227 Simplifying a = -1.203768227Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.453768227, -1.203768227}
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