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Simplifying -1.615x2 + 38.059x + -158.947 = 0 Reorder the terms: -158.947 + 38.059x + -1.615x2 = 0 Solving -158.947 + 38.059x + -1.615x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.615 the coefficient of the squared term: Divide each side by '-1.615'. 98.41919505 + -23.56594427x + x2 = 0 Move the constant term to the right: Add '-98.41919505' to each side of the equation. 98.41919505 + -23.56594427x + -98.41919505 + x2 = 0 + -98.41919505 Reorder the terms: 98.41919505 + -98.41919505 + -23.56594427x + x2 = 0 + -98.41919505 Combine like terms: 98.41919505 + -98.41919505 = 0.00000000 0.00000000 + -23.56594427x + x2 = 0 + -98.41919505 -23.56594427x + x2 = 0 + -98.41919505 Combine like terms: 0 + -98.41919505 = -98.41919505 -23.56594427x + x2 = -98.41919505 The x term is -23.56594427x. Take half its coefficient (-11.78297214). Square it (138.8384325) and add it to both sides. Add '138.8384325' to each side of the equation. -23.56594427x + 138.8384325 + x2 = -98.41919505 + 138.8384325 Reorder the terms: 138.8384325 + -23.56594427x + x2 = -98.41919505 + 138.8384325 Combine like terms: -98.41919505 + 138.8384325 = 40.41923745 138.8384325 + -23.56594427x + x2 = 40.41923745 Factor a perfect square on the left side: (x + -11.78297214)(x + -11.78297214) = 40.41923745 Calculate the square root of the right side: 6.357612559 Break this problem into two subproblems by setting (x + -11.78297214) equal to 6.357612559 and -6.357612559.Subproblem 1
x + -11.78297214 = 6.357612559 Simplifying x + -11.78297214 = 6.357612559 Reorder the terms: -11.78297214 + x = 6.357612559 Solving -11.78297214 + x = 6.357612559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.78297214' to each side of the equation. -11.78297214 + 11.78297214 + x = 6.357612559 + 11.78297214 Combine like terms: -11.78297214 + 11.78297214 = 0.00000000 0.00000000 + x = 6.357612559 + 11.78297214 x = 6.357612559 + 11.78297214 Combine like terms: 6.357612559 + 11.78297214 = 18.140584699 x = 18.140584699 Simplifying x = 18.140584699Subproblem 2
x + -11.78297214 = -6.357612559 Simplifying x + -11.78297214 = -6.357612559 Reorder the terms: -11.78297214 + x = -6.357612559 Solving -11.78297214 + x = -6.357612559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.78297214' to each side of the equation. -11.78297214 + 11.78297214 + x = -6.357612559 + 11.78297214 Combine like terms: -11.78297214 + 11.78297214 = 0.00000000 0.00000000 + x = -6.357612559 + 11.78297214 x = -6.357612559 + 11.78297214 Combine like terms: -6.357612559 + 11.78297214 = 5.425359581 x = 5.425359581 Simplifying x = 5.425359581Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.140584699, 5.425359581}
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