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Simplifying a2 + 4 + -1(-5) = a + 73 + -7 Multiply -1 * -5 a2 + 4 + 5 = a + 73 + -7 Reorder the terms: 4 + 5 + a2 = a + 73 + -7 Combine like terms: 4 + 5 = 9 9 + a2 = a + 73 + -7 Reorder the terms: 9 + a2 = 73 + -7 + a Combine like terms: 73 + -7 = 66 9 + a2 = 66 + a Solving 9 + a2 = 66 + a Solving for variable 'a'. Reorder the terms: 9 + -66 + -1a + a2 = 66 + a + -66 + -1a Combine like terms: 9 + -66 = -57 -57 + -1a + a2 = 66 + a + -66 + -1a Reorder the terms: -57 + -1a + a2 = 66 + -66 + a + -1a Combine like terms: 66 + -66 = 0 -57 + -1a + a2 = 0 + a + -1a -57 + -1a + a2 = a + -1a Combine like terms: a + -1a = 0 -57 + -1a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + -1a + 57 + a2 = 0 + 57 Reorder the terms: -57 + 57 + -1a + a2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + -1a + a2 = 0 + 57 -1a + a2 = 0 + 57 Combine like terms: 0 + 57 = 57 -1a + a2 = 57 The a term is -1a. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = 57 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 57 + 0.25 Combine like terms: 57 + 0.25 = 57.25 0.25 + -1a + a2 = 57.25 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (a + -0.5) equal to 7.566372975 and -7.566372975.Subproblem 1
a + -0.5 = 7.566372975 Simplifying a + -0.5 = 7.566372975 Reorder the terms: -0.5 + a = 7.566372975 Solving -0.5 + a = 7.566372975 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 7.566372975 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 7.566372975 + 0.5 a = 7.566372975 + 0.5 Combine like terms: 7.566372975 + 0.5 = 8.066372975 a = 8.066372975 Simplifying a = 8.066372975Subproblem 2
a + -0.5 = -7.566372975 Simplifying a + -0.5 = -7.566372975 Reorder the terms: -0.5 + a = -7.566372975 Solving -0.5 + a = -7.566372975 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -7.566372975 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -7.566372975 + 0.5 a = -7.566372975 + 0.5 Combine like terms: -7.566372975 + 0.5 = -7.066372975 a = -7.066372975 Simplifying a = -7.066372975Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.066372975, -7.066372975}
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