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Simplifying a(a + -773) = 148973 Reorder the terms: a(-773 + a) = 148973 (-773 * a + a * a) = 148973 (-773a + a2) = 148973 Solving -773a + a2 = 148973 Solving for variable 'a'. Reorder the terms: -148973 + -773a + a2 = 148973 + -148973 Combine like terms: 148973 + -148973 = 0 -148973 + -773a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '148973' to each side of the equation. -148973 + -773a + 148973 + a2 = 0 + 148973 Reorder the terms: -148973 + 148973 + -773a + a2 = 0 + 148973 Combine like terms: -148973 + 148973 = 0 0 + -773a + a2 = 0 + 148973 -773a + a2 = 0 + 148973 Combine like terms: 0 + 148973 = 148973 -773a + a2 = 148973 The a term is -773a. Take half its coefficient (-386.5). Square it (149382.25) and add it to both sides. Add '149382.25' to each side of the equation. -773a + 149382.25 + a2 = 148973 + 149382.25 Reorder the terms: 149382.25 + -773a + a2 = 148973 + 149382.25 Combine like terms: 148973 + 149382.25 = 298355.25 149382.25 + -773a + a2 = 298355.25 Factor a perfect square on the left side: (a + -386.5)(a + -386.5) = 298355.25 Calculate the square root of the right side: 546.219049466 Break this problem into two subproblems by setting (a + -386.5) equal to 546.219049466 and -546.219049466.Subproblem 1
a + -386.5 = 546.219049466 Simplifying a + -386.5 = 546.219049466 Reorder the terms: -386.5 + a = 546.219049466 Solving -386.5 + a = 546.219049466 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '386.5' to each side of the equation. -386.5 + 386.5 + a = 546.219049466 + 386.5 Combine like terms: -386.5 + 386.5 = 0.0 0.0 + a = 546.219049466 + 386.5 a = 546.219049466 + 386.5 Combine like terms: 546.219049466 + 386.5 = 932.719049466 a = 932.719049466 Simplifying a = 932.719049466Subproblem 2
a + -386.5 = -546.219049466 Simplifying a + -386.5 = -546.219049466 Reorder the terms: -386.5 + a = -546.219049466 Solving -386.5 + a = -546.219049466 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '386.5' to each side of the equation. -386.5 + 386.5 + a = -546.219049466 + 386.5 Combine like terms: -386.5 + 386.5 = 0.0 0.0 + a = -546.219049466 + 386.5 a = -546.219049466 + 386.5 Combine like terms: -546.219049466 + 386.5 = -159.719049466 a = -159.719049466 Simplifying a = -159.719049466Solution
The solution to the problem is based on the solutions from the subproblems. a = {932.719049466, -159.719049466}
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