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Simplifying 7x2 + -10x + -1 = 0 Reorder the terms: -1 + -10x + 7x2 = 0 Solving -1 + -10x + 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'. -0.1428571429 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -1.428571429x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -1.428571429x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -1.428571429x + x2 = 0 + 0.1428571429 -1.428571429x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -1.428571429x + x2 = 0.1428571429 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 0.1428571429 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 0.1428571429 + 0.5102040819 Combine like terms: 0.1428571429 + 0.5102040819 = 0.6530612248 0.5102040819 + -1.428571429x + x2 = 0.6530612248 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 0.6530612248 Calculate the square root of the right side: 0.808122036 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 0.808122036 and -0.808122036.Subproblem 1
x + -0.7142857145 = 0.808122036 Simplifying x + -0.7142857145 = 0.808122036 Reorder the terms: -0.7142857145 + x = 0.808122036 Solving -0.7142857145 + x = 0.808122036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 0.808122036 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.808122036 + 0.7142857145 x = 0.808122036 + 0.7142857145 Combine like terms: 0.808122036 + 0.7142857145 = 1.5224077505 x = 1.5224077505 Simplifying x = 1.5224077505Subproblem 2
x + -0.7142857145 = -0.808122036 Simplifying x + -0.7142857145 = -0.808122036 Reorder the terms: -0.7142857145 + x = -0.808122036 Solving -0.7142857145 + x = -0.808122036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -0.808122036 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.808122036 + 0.7142857145 x = -0.808122036 + 0.7142857145 Combine like terms: -0.808122036 + 0.7142857145 = -0.0938363215 x = -0.0938363215 Simplifying x = -0.0938363215Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5224077505, -0.0938363215}
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