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Simplifying 35x2 + -32x + -104 = 0 Reorder the terms: -104 + -32x + 35x2 = 0 Solving -104 + -32x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -2.971428571 + -0.9142857143x + x2 = 0 Move the constant term to the right: Add '2.971428571' to each side of the equation. -2.971428571 + -0.9142857143x + 2.971428571 + x2 = 0 + 2.971428571 Reorder the terms: -2.971428571 + 2.971428571 + -0.9142857143x + x2 = 0 + 2.971428571 Combine like terms: -2.971428571 + 2.971428571 = 0.000000000 0.000000000 + -0.9142857143x + x2 = 0 + 2.971428571 -0.9142857143x + x2 = 0 + 2.971428571 Combine like terms: 0 + 2.971428571 = 2.971428571 -0.9142857143x + x2 = 2.971428571 The x term is -0.9142857143x. Take half its coefficient (-0.4571428572). Square it (0.2089795919) and add it to both sides. Add '0.2089795919' to each side of the equation. -0.9142857143x + 0.2089795919 + x2 = 2.971428571 + 0.2089795919 Reorder the terms: 0.2089795919 + -0.9142857143x + x2 = 2.971428571 + 0.2089795919 Combine like terms: 2.971428571 + 0.2089795919 = 3.1804081629 0.2089795919 + -0.9142857143x + x2 = 3.1804081629 Factor a perfect square on the left side: (x + -0.4571428572)(x + -0.4571428572) = 3.1804081629 Calculate the square root of the right side: 1.78336989 Break this problem into two subproblems by setting (x + -0.4571428572) equal to 1.78336989 and -1.78336989.Subproblem 1
x + -0.4571428572 = 1.78336989 Simplifying x + -0.4571428572 = 1.78336989 Reorder the terms: -0.4571428572 + x = 1.78336989 Solving -0.4571428572 + x = 1.78336989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4571428572' to each side of the equation. -0.4571428572 + 0.4571428572 + x = 1.78336989 + 0.4571428572 Combine like terms: -0.4571428572 + 0.4571428572 = 0.0000000000 0.0000000000 + x = 1.78336989 + 0.4571428572 x = 1.78336989 + 0.4571428572 Combine like terms: 1.78336989 + 0.4571428572 = 2.2405127472 x = 2.2405127472 Simplifying x = 2.2405127472Subproblem 2
x + -0.4571428572 = -1.78336989 Simplifying x + -0.4571428572 = -1.78336989 Reorder the terms: -0.4571428572 + x = -1.78336989 Solving -0.4571428572 + x = -1.78336989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4571428572' to each side of the equation. -0.4571428572 + 0.4571428572 + x = -1.78336989 + 0.4571428572 Combine like terms: -0.4571428572 + 0.4571428572 = 0.0000000000 0.0000000000 + x = -1.78336989 + 0.4571428572 x = -1.78336989 + 0.4571428572 Combine like terms: -1.78336989 + 0.4571428572 = -1.3262270328 x = -1.3262270328 Simplifying x = -1.3262270328Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2405127472, -1.3262270328}
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