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Simplifying 7x2 + -60x + -50 = 0 Reorder the terms: -50 + -60x + 7x2 = 0 Solving -50 + -60x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -7.142857143 + -8.571428571x + x2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + -8.571428571x + 7.142857143 + x2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + -8.571428571x + x2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + -8.571428571x + x2 = 0 + 7.142857143 -8.571428571x + x2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 -8.571428571x + x2 = 7.142857143 The x term is -8.571428571x. Take half its coefficient (-4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. -8.571428571x + 18.36734694 + x2 = 7.142857143 + 18.36734694 Reorder the terms: 18.36734694 + -8.571428571x + x2 = 7.142857143 + 18.36734694 Combine like terms: 7.142857143 + 18.36734694 = 25.510204083 18.36734694 + -8.571428571x + x2 = 25.510204083 Factor a perfect square on the left side: (x + -4.285714286)(x + -4.285714286) = 25.510204083 Calculate the square root of the right side: 5.050762723 Break this problem into two subproblems by setting (x + -4.285714286) equal to 5.050762723 and -5.050762723.Subproblem 1
x + -4.285714286 = 5.050762723 Simplifying x + -4.285714286 = 5.050762723 Reorder the terms: -4.285714286 + x = 5.050762723 Solving -4.285714286 + x = 5.050762723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = 5.050762723 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = 5.050762723 + 4.285714286 x = 5.050762723 + 4.285714286 Combine like terms: 5.050762723 + 4.285714286 = 9.336477009 x = 9.336477009 Simplifying x = 9.336477009Subproblem 2
x + -4.285714286 = -5.050762723 Simplifying x + -4.285714286 = -5.050762723 Reorder the terms: -4.285714286 + x = -5.050762723 Solving -4.285714286 + x = -5.050762723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = -5.050762723 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = -5.050762723 + 4.285714286 x = -5.050762723 + 4.285714286 Combine like terms: -5.050762723 + 4.285714286 = -0.765048437 x = -0.765048437 Simplifying x = -0.765048437Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.336477009, -0.765048437}
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