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Simplifying -7x20 + -10x10 + 6 = 0 Reorder the terms: 6 + -10x10 + -7x20 = 0 Solving 6 + -10x10 + -7x20 = 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'. -0.8571428571 + 1.428571429x10 + x20 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 1.428571429x10 + 0.8571428571 + x20 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 1.428571429x10 + x20 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 1.428571429x10 + x20 = 0 + 0.8571428571 1.428571429x10 + x20 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 1.428571429x10 + x20 = 0.8571428571 The x term is 1.428571429x10. 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. 1.428571429x10 + 0.5102040819 + x20 = 0.8571428571 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x10 + x20 = 0.8571428571 + 0.5102040819 Combine like terms: 0.8571428571 + 0.5102040819 = 1.367346939 0.5102040819 + 1.428571429x10 + x20 = 1.367346939 Factor a perfect square on the left side: (x10 + 0.7142857145)(x10 + 0.7142857145) = 1.367346939 Calculate the square root of the right side: 1.16933611 Break this problem into two subproblems by setting (x10 + 0.7142857145) equal to 1.16933611 and -1.16933611.Subproblem 1
x10 + 0.7142857145 = 1.16933611 Simplifying x10 + 0.7142857145 = 1.16933611 Reorder the terms: 0.7142857145 + x10 = 1.16933611 Solving 0.7142857145 + x10 = 1.16933611 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 + x10 = 1.16933611 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x10 = 1.16933611 + -0.7142857145 x10 = 1.16933611 + -0.7142857145 Combine like terms: 1.16933611 + -0.7142857145 = 0.4550503955 x10 = 0.4550503955 Simplifying x10 = 0.4550503955 Reorder the terms: -0.4550503955 + x10 = 0.4550503955 + -0.4550503955 Combine like terms: 0.4550503955 + -0.4550503955 = 0.0000000000 -0.4550503955 + x10 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x10 + 0.7142857145 = -1.16933611 Simplifying x10 + 0.7142857145 = -1.16933611 Reorder the terms: 0.7142857145 + x10 = -1.16933611 Solving 0.7142857145 + x10 = -1.16933611 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 + x10 = -1.16933611 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x10 = -1.16933611 + -0.7142857145 x10 = -1.16933611 + -0.7142857145 Combine like terms: -1.16933611 + -0.7142857145 = -1.8836218245 x10 = -1.8836218245 Simplifying x10 = -1.8836218245 Reorder the terms: 1.8836218245 + x10 = -1.8836218245 + 1.8836218245 Combine like terms: -1.8836218245 + 1.8836218245 = 0.0000000000 1.8836218245 + x10 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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