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Simplifying 7x2 + -1x + -34 = 0 Reorder the terms: -34 + -1x + 7x2 = 0 Solving -34 + -1x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.857142857 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '4.857142857' to each side of the equation. -4.857142857 + -0.1428571429x + 4.857142857 + x2 = 0 + 4.857142857 Reorder the terms: -4.857142857 + 4.857142857 + -0.1428571429x + x2 = 0 + 4.857142857 Combine like terms: -4.857142857 + 4.857142857 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 4.857142857 -0.1428571429x + x2 = 0 + 4.857142857 Combine like terms: 0 + 4.857142857 = 4.857142857 -0.1428571429x + x2 = 4.857142857 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 = 4.857142857 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 4.857142857 + 0.005102040819 Combine like terms: 4.857142857 + 0.005102040819 = 4.862244897819 0.005102040819 + -0.1428571429x + x2 = 4.862244897819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 4.862244897819 Calculate the square root of the right side: 2.205049863 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 2.205049863 and -2.205049863.Subproblem 1
x + -0.07142857145 = 2.205049863 Simplifying x + -0.07142857145 = 2.205049863 Reorder the terms: -0.07142857145 + x = 2.205049863 Solving -0.07142857145 + x = 2.205049863 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 = 2.205049863 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 2.205049863 + 0.07142857145 x = 2.205049863 + 0.07142857145 Combine like terms: 2.205049863 + 0.07142857145 = 2.27647843445 x = 2.27647843445 Simplifying x = 2.27647843445Subproblem 2
x + -0.07142857145 = -2.205049863 Simplifying x + -0.07142857145 = -2.205049863 Reorder the terms: -0.07142857145 + x = -2.205049863 Solving -0.07142857145 + x = -2.205049863 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 = -2.205049863 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -2.205049863 + 0.07142857145 x = -2.205049863 + 0.07142857145 Combine like terms: -2.205049863 + 0.07142857145 = -2.13362129155 x = -2.13362129155 Simplifying x = -2.13362129155Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.27647843445, -2.13362129155}
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