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Simplifying 4a(a + 63) = 4a + -63 Reorder the terms: 4a(63 + a) = 4a + -63 (63 * 4a + a * 4a) = 4a + -63 (252a + 4a2) = 4a + -63 Reorder the terms: 252a + 4a2 = -63 + 4a Solving 252a + 4a2 = -63 + 4a Solving for variable 'a'. Reorder the terms: 63 + 252a + -4a + 4a2 = -63 + 4a + 63 + -4a Combine like terms: 252a + -4a = 248a 63 + 248a + 4a2 = -63 + 4a + 63 + -4a Reorder the terms: 63 + 248a + 4a2 = -63 + 63 + 4a + -4a Combine like terms: -63 + 63 = 0 63 + 248a + 4a2 = 0 + 4a + -4a 63 + 248a + 4a2 = 4a + -4a Combine like terms: 4a + -4a = 0 63 + 248a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 15.75 + 62a + a2 = 0 Move the constant term to the right: Add '-15.75' to each side of the equation. 15.75 + 62a + -15.75 + a2 = 0 + -15.75 Reorder the terms: 15.75 + -15.75 + 62a + a2 = 0 + -15.75 Combine like terms: 15.75 + -15.75 = 0.00 0.00 + 62a + a2 = 0 + -15.75 62a + a2 = 0 + -15.75 Combine like terms: 0 + -15.75 = -15.75 62a + a2 = -15.75 The a term is 62a. Take half its coefficient (31). Square it (961) and add it to both sides. Add '961' to each side of the equation. 62a + 961 + a2 = -15.75 + 961 Reorder the terms: 961 + 62a + a2 = -15.75 + 961 Combine like terms: -15.75 + 961 = 945.25 961 + 62a + a2 = 945.25 Factor a perfect square on the left side: (a + 31)(a + 31) = 945.25 Calculate the square root of the right side: 30.744918279 Break this problem into two subproblems by setting (a + 31) equal to 30.744918279 and -30.744918279.Subproblem 1
a + 31 = 30.744918279 Simplifying a + 31 = 30.744918279 Reorder the terms: 31 + a = 30.744918279 Solving 31 + a = 30.744918279 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + a = 30.744918279 + -31 Combine like terms: 31 + -31 = 0 0 + a = 30.744918279 + -31 a = 30.744918279 + -31 Combine like terms: 30.744918279 + -31 = -0.255081721 a = -0.255081721 Simplifying a = -0.255081721Subproblem 2
a + 31 = -30.744918279 Simplifying a + 31 = -30.744918279 Reorder the terms: 31 + a = -30.744918279 Solving 31 + a = -30.744918279 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + a = -30.744918279 + -31 Combine like terms: 31 + -31 = 0 0 + a = -30.744918279 + -31 a = -30.744918279 + -31 Combine like terms: -30.744918279 + -31 = -61.744918279 a = -61.744918279 Simplifying a = -61.744918279Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.255081721, -61.744918279}
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