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Simplifying 10 = 7x(7x + -18) Reorder the terms: 10 = 7x(-18 + 7x) 10 = (-18 * 7x + 7x * 7x) 10 = (-126x + 49x2) Solving 10 = -126x + 49x2 Solving for variable 'x'. Reorder the terms: 10 + 126x + -49x2 = -126x + 126x + 49x2 + -49x2 Combine like terms: -126x + 126x = 0 10 + 126x + -49x2 = 0 + 49x2 + -49x2 10 + 126x + -49x2 = 49x2 + -49x2 Combine like terms: 49x2 + -49x2 = 0 10 + 126x + -49x2 = 0 Begin completing the square. Divide all terms by -49 the coefficient of the squared term: Divide each side by '-49'. -0.2040816327 + -2.571428571x + x2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -2.571428571x + 0.2040816327 + x2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -2.571428571x + x2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -2.571428571x + x2 = 0 + 0.2040816327 -2.571428571x + x2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -2.571428571x + x2 = 0.2040816327 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 = 0.2040816327 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571x + x2 = 0.2040816327 + 1.653061225 Combine like terms: 0.2040816327 + 1.653061225 = 1.8571428577 1.653061225 + -2.571428571x + x2 = 1.8571428577 Factor a perfect square on the left side: (x + -1.285714286)(x + -1.285714286) = 1.8571428577 Calculate the square root of the right side: 1.362770288 Break this problem into two subproblems by setting (x + -1.285714286) equal to 1.362770288 and -1.362770288.Subproblem 1
x + -1.285714286 = 1.362770288 Simplifying x + -1.285714286 = 1.362770288 Reorder the terms: -1.285714286 + x = 1.362770288 Solving -1.285714286 + x = 1.362770288 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 = 1.362770288 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = 1.362770288 + 1.285714286 x = 1.362770288 + 1.285714286 Combine like terms: 1.362770288 + 1.285714286 = 2.648484574 x = 2.648484574 Simplifying x = 2.648484574Subproblem 2
x + -1.285714286 = -1.362770288 Simplifying x + -1.285714286 = -1.362770288 Reorder the terms: -1.285714286 + x = -1.362770288 Solving -1.285714286 + x = -1.362770288 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 = -1.362770288 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = -1.362770288 + 1.285714286 x = -1.362770288 + 1.285714286 Combine like terms: -1.362770288 + 1.285714286 = -0.077056002 x = -0.077056002 Simplifying x = -0.077056002Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.648484574, -0.077056002}
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