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Simplifying 7.45x2 + 3.11x = 5.22 Reorder the terms: 3.11x + 7.45x2 = 5.22 Solving 3.11x + 7.45x2 = 5.22 Solving for variable 'x'. Reorder the terms: -5.22 + 3.11x + 7.45x2 = 5.22 + -5.22 Combine like terms: 5.22 + -5.22 = 0.00 -5.22 + 3.11x + 7.45x2 = 0.00 Begin completing the square. Divide all terms by 7.45 the coefficient of the squared term: Divide each side by '7.45'. -0.7006711409 + 0.4174496644x + x2 = 0 Move the constant term to the right: Add '0.7006711409' to each side of the equation. -0.7006711409 + 0.4174496644x + 0.7006711409 + x2 = 0 + 0.7006711409 Reorder the terms: -0.7006711409 + 0.7006711409 + 0.4174496644x + x2 = 0 + 0.7006711409 Combine like terms: -0.7006711409 + 0.7006711409 = 0.0000000000 0.0000000000 + 0.4174496644x + x2 = 0 + 0.7006711409 0.4174496644x + x2 = 0 + 0.7006711409 Combine like terms: 0 + 0.7006711409 = 0.7006711409 0.4174496644x + x2 = 0.7006711409 The x term is 0.4174496644x. Take half its coefficient (0.2087248322). Square it (0.04356605558) and add it to both sides. Add '0.04356605558' to each side of the equation. 0.4174496644x + 0.04356605558 + x2 = 0.7006711409 + 0.04356605558 Reorder the terms: 0.04356605558 + 0.4174496644x + x2 = 0.7006711409 + 0.04356605558 Combine like terms: 0.7006711409 + 0.04356605558 = 0.74423719648 0.04356605558 + 0.4174496644x + x2 = 0.74423719648 Factor a perfect square on the left side: (x + 0.2087248322)(x + 0.2087248322) = 0.74423719648 Calculate the square root of the right side: 0.862691832 Break this problem into two subproblems by setting (x + 0.2087248322) equal to 0.862691832 and -0.862691832.Subproblem 1
x + 0.2087248322 = 0.862691832 Simplifying x + 0.2087248322 = 0.862691832 Reorder the terms: 0.2087248322 + x = 0.862691832 Solving 0.2087248322 + x = 0.862691832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2087248322' to each side of the equation. 0.2087248322 + -0.2087248322 + x = 0.862691832 + -0.2087248322 Combine like terms: 0.2087248322 + -0.2087248322 = 0.0000000000 0.0000000000 + x = 0.862691832 + -0.2087248322 x = 0.862691832 + -0.2087248322 Combine like terms: 0.862691832 + -0.2087248322 = 0.6539669998 x = 0.6539669998 Simplifying x = 0.6539669998Subproblem 2
x + 0.2087248322 = -0.862691832 Simplifying x + 0.2087248322 = -0.862691832 Reorder the terms: 0.2087248322 + x = -0.862691832 Solving 0.2087248322 + x = -0.862691832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2087248322' to each side of the equation. 0.2087248322 + -0.2087248322 + x = -0.862691832 + -0.2087248322 Combine like terms: 0.2087248322 + -0.2087248322 = 0.0000000000 0.0000000000 + x = -0.862691832 + -0.2087248322 x = -0.862691832 + -0.2087248322 Combine like terms: -0.862691832 + -0.2087248322 = -1.0714166642 x = -1.0714166642 Simplifying x = -1.0714166642Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6539669998, -1.0714166642}
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