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Simplifying 7x2 + -25x + -24 = 0 Reorder the terms: -24 + -25x + 7x2 = 0 Solving -24 + -25x + 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'. -3.428571429 + -3.571428571x + x2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -3.571428571x + 3.428571429 + x2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -3.571428571x + x2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -3.571428571x + x2 = 0 + 3.428571429 -3.571428571x + x2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -3.571428571x + x2 = 3.428571429 The x term is -3.571428571x. Take half its coefficient (-1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. -3.571428571x + 3.188775511 + x2 = 3.428571429 + 3.188775511 Reorder the terms: 3.188775511 + -3.571428571x + x2 = 3.428571429 + 3.188775511 Combine like terms: 3.428571429 + 3.188775511 = 6.61734694 3.188775511 + -3.571428571x + x2 = 6.61734694 Factor a perfect square on the left side: (x + -1.785714286)(x + -1.785714286) = 6.61734694 Calculate the square root of the right side: 2.572420444 Break this problem into two subproblems by setting (x + -1.785714286) equal to 2.572420444 and -2.572420444.Subproblem 1
x + -1.785714286 = 2.572420444 Simplifying x + -1.785714286 = 2.572420444 Reorder the terms: -1.785714286 + x = 2.572420444 Solving -1.785714286 + x = 2.572420444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = 2.572420444 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 2.572420444 + 1.785714286 x = 2.572420444 + 1.785714286 Combine like terms: 2.572420444 + 1.785714286 = 4.35813473 x = 4.35813473 Simplifying x = 4.35813473Subproblem 2
x + -1.785714286 = -2.572420444 Simplifying x + -1.785714286 = -2.572420444 Reorder the terms: -1.785714286 + x = -2.572420444 Solving -1.785714286 + x = -2.572420444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = -2.572420444 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -2.572420444 + 1.785714286 x = -2.572420444 + 1.785714286 Combine like terms: -2.572420444 + 1.785714286 = -0.786706158 x = -0.786706158 Simplifying x = -0.786706158Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.35813473, -0.786706158}
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