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Simplifying 35x2 + -5x + -200 = 0 Reorder the terms: -200 + -5x + 35x2 = 0 Solving -200 + -5x + 35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-40 + -1x + 7x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-40 + -1x + 7x2)' equal to zero and attempt to solve: Simplifying -40 + -1x + 7x2 = 0 Solving -40 + -1x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.714285714 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + -0.1428571429x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + -0.1428571429x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 5.714285714 -0.1428571429x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 -0.1428571429x + x2 = 5.714285714 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 5.714285714 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 5.714285714 + 0.005102040819 Combine like terms: 5.714285714 + 0.005102040819 = 5.719387754819 0.005102040819 + -0.1428571429x + x2 = 5.719387754819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 5.719387754819 Calculate the square root of the right side: 2.391524149 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 2.391524149 and -2.391524149.Subproblem 1
x + -0.07142857145 = 2.391524149 Simplifying x + -0.07142857145 = 2.391524149 Reorder the terms: -0.07142857145 + x = 2.391524149 Solving -0.07142857145 + x = 2.391524149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 2.391524149 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 2.391524149 + 0.07142857145 x = 2.391524149 + 0.07142857145 Combine like terms: 2.391524149 + 0.07142857145 = 2.46295272045 x = 2.46295272045 Simplifying x = 2.46295272045Subproblem 2
x + -0.07142857145 = -2.391524149 Simplifying x + -0.07142857145 = -2.391524149 Reorder the terms: -0.07142857145 + x = -2.391524149 Solving -0.07142857145 + x = -2.391524149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -2.391524149 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -2.391524149 + 0.07142857145 x = -2.391524149 + 0.07142857145 Combine like terms: -2.391524149 + 0.07142857145 = -2.32009557755 x = -2.32009557755 Simplifying x = -2.32009557755Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.46295272045, -2.32009557755}Solution
x = {2.46295272045, -2.32009557755}
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