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Simplifying 23x + 3.50x2 = 117.72 Solving 23x + 3.50x2 = 117.72 Solving for variable 'x'. Reorder the terms: -117.72 + 23x + 3.50x2 = 117.72 + -117.72 Combine like terms: 117.72 + -117.72 = 0.00 -117.72 + 23x + 3.50x2 = 0.00 Begin completing the square. Divide all terms by 3.50 the coefficient of the squared term: Divide each side by '3.50'. -33.63428571 + 6.571428571x + x2 = 0 Move the constant term to the right: Add '33.63428571' to each side of the equation. -33.63428571 + 6.571428571x + 33.63428571 + x2 = 0 + 33.63428571 Reorder the terms: -33.63428571 + 33.63428571 + 6.571428571x + x2 = 0 + 33.63428571 Combine like terms: -33.63428571 + 33.63428571 = 0.00000000 0.00000000 + 6.571428571x + x2 = 0 + 33.63428571 6.571428571x + x2 = 0 + 33.63428571 Combine like terms: 0 + 33.63428571 = 33.63428571 6.571428571x + x2 = 33.63428571 The x term is 6.571428571x. Take half its coefficient (3.285714286). Square it (10.79591837) and add it to both sides. Add '10.79591837' to each side of the equation. 6.571428571x + 10.79591837 + x2 = 33.63428571 + 10.79591837 Reorder the terms: 10.79591837 + 6.571428571x + x2 = 33.63428571 + 10.79591837 Combine like terms: 33.63428571 + 10.79591837 = 44.43020408 10.79591837 + 6.571428571x + x2 = 44.43020408 Factor a perfect square on the left side: (x + 3.285714286)(x + 3.285714286) = 44.43020408 Calculate the square root of the right side: 6.665598554 Break this problem into two subproblems by setting (x + 3.285714286) equal to 6.665598554 and -6.665598554.Subproblem 1
x + 3.285714286 = 6.665598554 Simplifying x + 3.285714286 = 6.665598554 Reorder the terms: 3.285714286 + x = 6.665598554 Solving 3.285714286 + x = 6.665598554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.285714286' to each side of the equation. 3.285714286 + -3.285714286 + x = 6.665598554 + -3.285714286 Combine like terms: 3.285714286 + -3.285714286 = 0.000000000 0.000000000 + x = 6.665598554 + -3.285714286 x = 6.665598554 + -3.285714286 Combine like terms: 6.665598554 + -3.285714286 = 3.379884268 x = 3.379884268 Simplifying x = 3.379884268Subproblem 2
x + 3.285714286 = -6.665598554 Simplifying x + 3.285714286 = -6.665598554 Reorder the terms: 3.285714286 + x = -6.665598554 Solving 3.285714286 + x = -6.665598554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.285714286' to each side of the equation. 3.285714286 + -3.285714286 + x = -6.665598554 + -3.285714286 Combine like terms: 3.285714286 + -3.285714286 = 0.000000000 0.000000000 + x = -6.665598554 + -3.285714286 x = -6.665598554 + -3.285714286 Combine like terms: -6.665598554 + -3.285714286 = -9.95131284 x = -9.95131284 Simplifying x = -9.95131284Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.379884268, -9.95131284}
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