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Simplifying 7x(5x + 9) = 18 + -1(x + 9) Reorder the terms: 7x(9 + 5x) = 18 + -1(x + 9) (9 * 7x + 5x * 7x) = 18 + -1(x + 9) (63x + 35x2) = 18 + -1(x + 9) Reorder the terms: 63x + 35x2 = 18 + -1(9 + x) 63x + 35x2 = 18 + (9 * -1 + x * -1) 63x + 35x2 = 18 + (-9 + -1x) Combine like terms: 18 + -9 = 9 63x + 35x2 = 9 + -1x Solving 63x + 35x2 = 9 + -1x Solving for variable 'x'. Reorder the terms: -9 + 63x + x + 35x2 = 9 + -1x + -9 + x Combine like terms: 63x + x = 64x -9 + 64x + 35x2 = 9 + -1x + -9 + x Reorder the terms: -9 + 64x + 35x2 = 9 + -9 + -1x + x Combine like terms: 9 + -9 = 0 -9 + 64x + 35x2 = 0 + -1x + x -9 + 64x + 35x2 = -1x + x Combine like terms: -1x + x = 0 -9 + 64x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.2571428571 + 1.828571429x + x2 = 0 Move the constant term to the right: Add '0.2571428571' to each side of the equation. -0.2571428571 + 1.828571429x + 0.2571428571 + x2 = 0 + 0.2571428571 Reorder the terms: -0.2571428571 + 0.2571428571 + 1.828571429x + x2 = 0 + 0.2571428571 Combine like terms: -0.2571428571 + 0.2571428571 = 0.0000000000 0.0000000000 + 1.828571429x + x2 = 0 + 0.2571428571 1.828571429x + x2 = 0 + 0.2571428571 Combine like terms: 0 + 0.2571428571 = 0.2571428571 1.828571429x + x2 = 0.2571428571 The x term is 1.828571429x. Take half its coefficient (0.9142857145). Square it (0.8359183677) and add it to both sides. Add '0.8359183677' to each side of the equation. 1.828571429x + 0.8359183677 + x2 = 0.2571428571 + 0.8359183677 Reorder the terms: 0.8359183677 + 1.828571429x + x2 = 0.2571428571 + 0.8359183677 Combine like terms: 0.2571428571 + 0.8359183677 = 1.0930612248 0.8359183677 + 1.828571429x + x2 = 1.0930612248 Factor a perfect square on the left side: (x + 0.9142857145)(x + 0.9142857145) = 1.0930612248 Calculate the square root of the right side: 1.045495684 Break this problem into two subproblems by setting (x + 0.9142857145) equal to 1.045495684 and -1.045495684.Subproblem 1
x + 0.9142857145 = 1.045495684 Simplifying x + 0.9142857145 = 1.045495684 Reorder the terms: 0.9142857145 + x = 1.045495684 Solving 0.9142857145 + x = 1.045495684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9142857145' to each side of the equation. 0.9142857145 + -0.9142857145 + x = 1.045495684 + -0.9142857145 Combine like terms: 0.9142857145 + -0.9142857145 = 0.0000000000 0.0000000000 + x = 1.045495684 + -0.9142857145 x = 1.045495684 + -0.9142857145 Combine like terms: 1.045495684 + -0.9142857145 = 0.1312099695 x = 0.1312099695 Simplifying x = 0.1312099695Subproblem 2
x + 0.9142857145 = -1.045495684 Simplifying x + 0.9142857145 = -1.045495684 Reorder the terms: 0.9142857145 + x = -1.045495684 Solving 0.9142857145 + x = -1.045495684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9142857145' to each side of the equation. 0.9142857145 + -0.9142857145 + x = -1.045495684 + -0.9142857145 Combine like terms: 0.9142857145 + -0.9142857145 = 0.0000000000 0.0000000000 + x = -1.045495684 + -0.9142857145 x = -1.045495684 + -0.9142857145 Combine like terms: -1.045495684 + -0.9142857145 = -1.9597813985 x = -1.9597813985 Simplifying x = -1.9597813985Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1312099695, -1.9597813985}
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