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Simplifying 35x2 + -100x + -5 = 0 Reorder the terms: -5 + -100x + 35x2 = 0 Solving -5 + -100x + 35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + -20x + 7x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -20x + 7x2)' equal to zero and attempt to solve: Simplifying -1 + -20x + 7x2 = 0 Solving -1 + -20x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -2.857142857x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -2.857142857x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -2.857142857x + x2 = 0 + 0.1428571429 -2.857142857x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -2.857142857x + x2 = 0.1428571429 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 0.1428571429 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 0.1428571429 + 2.040816328 Combine like terms: 0.1428571429 + 2.040816328 = 2.1836734709 2.040816328 + -2.857142857x + x2 = 2.1836734709 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 2.1836734709 Calculate the square root of the right side: 1.477725777 Break this problem into two subproblems by setting (x + -1.428571429) equal to 1.477725777 and -1.477725777.Subproblem 1
x + -1.428571429 = 1.477725777 Simplifying x + -1.428571429 = 1.477725777 Reorder the terms: -1.428571429 + x = 1.477725777 Solving -1.428571429 + x = 1.477725777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 1.477725777 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 1.477725777 + 1.428571429 x = 1.477725777 + 1.428571429 Combine like terms: 1.477725777 + 1.428571429 = 2.906297206 x = 2.906297206 Simplifying x = 2.906297206Subproblem 2
x + -1.428571429 = -1.477725777 Simplifying x + -1.428571429 = -1.477725777 Reorder the terms: -1.428571429 + x = -1.477725777 Solving -1.428571429 + x = -1.477725777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -1.477725777 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -1.477725777 + 1.428571429 x = -1.477725777 + 1.428571429 Combine like terms: -1.477725777 + 1.428571429 = -0.049154348 x = -0.049154348 Simplifying x = -0.049154348Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.906297206, -0.049154348}Solution
x = {2.906297206, -0.049154348}
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