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Simplifying 63x2 + -73x + -625 = 0 Reorder the terms: -625 + -73x + 63x2 = 0 Solving -625 + -73x + 63x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -9.920634921 + -1.158730159x + x2 = 0 Move the constant term to the right: Add '9.920634921' to each side of the equation. -9.920634921 + -1.158730159x + 9.920634921 + x2 = 0 + 9.920634921 Reorder the terms: -9.920634921 + 9.920634921 + -1.158730159x + x2 = 0 + 9.920634921 Combine like terms: -9.920634921 + 9.920634921 = 0.000000000 0.000000000 + -1.158730159x + x2 = 0 + 9.920634921 -1.158730159x + x2 = 0 + 9.920634921 Combine like terms: 0 + 9.920634921 = 9.920634921 -1.158730159x + x2 = 9.920634921 The x term is -1.158730159x. Take half its coefficient (-0.5793650795). Square it (0.3356638953) and add it to both sides. Add '0.3356638953' to each side of the equation. -1.158730159x + 0.3356638953 + x2 = 9.920634921 + 0.3356638953 Reorder the terms: 0.3356638953 + -1.158730159x + x2 = 9.920634921 + 0.3356638953 Combine like terms: 9.920634921 + 0.3356638953 = 10.2562988163 0.3356638953 + -1.158730159x + x2 = 10.2562988163 Factor a perfect square on the left side: (x + -0.5793650795)(x + -0.5793650795) = 10.2562988163 Calculate the square root of the right side: 3.202545677 Break this problem into two subproblems by setting (x + -0.5793650795) equal to 3.202545677 and -3.202545677.Subproblem 1
x + -0.5793650795 = 3.202545677 Simplifying x + -0.5793650795 = 3.202545677 Reorder the terms: -0.5793650795 + x = 3.202545677 Solving -0.5793650795 + x = 3.202545677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5793650795' to each side of the equation. -0.5793650795 + 0.5793650795 + x = 3.202545677 + 0.5793650795 Combine like terms: -0.5793650795 + 0.5793650795 = 0.0000000000 0.0000000000 + x = 3.202545677 + 0.5793650795 x = 3.202545677 + 0.5793650795 Combine like terms: 3.202545677 + 0.5793650795 = 3.7819107565 x = 3.7819107565 Simplifying x = 3.7819107565Subproblem 2
x + -0.5793650795 = -3.202545677 Simplifying x + -0.5793650795 = -3.202545677 Reorder the terms: -0.5793650795 + x = -3.202545677 Solving -0.5793650795 + x = -3.202545677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5793650795' to each side of the equation. -0.5793650795 + 0.5793650795 + x = -3.202545677 + 0.5793650795 Combine like terms: -0.5793650795 + 0.5793650795 = 0.0000000000 0.0000000000 + x = -3.202545677 + 0.5793650795 x = -3.202545677 + 0.5793650795 Combine like terms: -3.202545677 + 0.5793650795 = -2.6231805975 x = -2.6231805975 Simplifying x = -2.6231805975Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.7819107565, -2.6231805975}
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