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Simplifying 14x2 + 36x = 38.75 Reorder the terms: 36x + 14x2 = 38.75 Solving 36x + 14x2 = 38.75 Solving for variable 'x'. Reorder the terms: -38.75 + 36x + 14x2 = 38.75 + -38.75 Combine like terms: 38.75 + -38.75 = 0.00 -38.75 + 36x + 14x2 = 0.00 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -2.767857143 + 2.571428571x + x2 = 0.00 Move the constant term to the right: Add '2.767857143' to each side of the equation. -2.767857143 + 2.571428571x + 2.767857143 + x2 = 0.00 + 2.767857143 Reorder the terms: -2.767857143 + 2.767857143 + 2.571428571x + x2 = 0.00 + 2.767857143 Combine like terms: -2.767857143 + 2.767857143 = 0.000000000 0.000000000 + 2.571428571x + x2 = 0.00 + 2.767857143 2.571428571x + x2 = 0.00 + 2.767857143 Combine like terms: 0.00 + 2.767857143 = 2.767857143 2.571428571x + x2 = 2.767857143 The x term is 2.571428571x. Take half its coefficient (1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. 2.571428571x + 1.653061225 + x2 = 2.767857143 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = 2.767857143 + 1.653061225 Combine like terms: 2.767857143 + 1.653061225 = 4.420918368 1.653061225 + 2.571428571x + x2 = 4.420918368 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 4.420918368 Calculate the square root of the right side: 2.102598004 Break this problem into two subproblems by setting (x + 1.285714286) equal to 2.102598004 and -2.102598004.Subproblem 1
x + 1.285714286 = 2.102598004 Simplifying x + 1.285714286 = 2.102598004 Reorder the terms: 1.285714286 + x = 2.102598004 Solving 1.285714286 + x = 2.102598004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = 2.102598004 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 2.102598004 + -1.285714286 x = 2.102598004 + -1.285714286 Combine like terms: 2.102598004 + -1.285714286 = 0.816883718 x = 0.816883718 Simplifying x = 0.816883718Subproblem 2
x + 1.285714286 = -2.102598004 Simplifying x + 1.285714286 = -2.102598004 Reorder the terms: 1.285714286 + x = -2.102598004 Solving 1.285714286 + x = -2.102598004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = -2.102598004 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -2.102598004 + -1.285714286 x = -2.102598004 + -1.285714286 Combine like terms: -2.102598004 + -1.285714286 = -3.38831229 x = -3.38831229 Simplifying x = -3.38831229Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.816883718, -3.38831229}
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