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Simplifying 7x2 + -54x + -6 = 0 Reorder the terms: -6 + -54x + 7x2 = 0 Solving -6 + -54x + 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'. -0.8571428571 + -7.714285714x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -7.714285714x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -7.714285714x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -7.714285714x + x2 = 0 + 0.8571428571 -7.714285714x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -7.714285714x + x2 = 0.8571428571 The x term is -7.714285714x. Take half its coefficient (-3.857142857). Square it (14.87755102) and add it to both sides. Add '14.87755102' to each side of the equation. -7.714285714x + 14.87755102 + x2 = 0.8571428571 + 14.87755102 Reorder the terms: 14.87755102 + -7.714285714x + x2 = 0.8571428571 + 14.87755102 Combine like terms: 0.8571428571 + 14.87755102 = 15.7346938771 14.87755102 + -7.714285714x + x2 = 15.7346938771 Factor a perfect square on the left side: (x + -3.857142857)(x + -3.857142857) = 15.7346938771 Calculate the square root of the right side: 3.966698108 Break this problem into two subproblems by setting (x + -3.857142857) equal to 3.966698108 and -3.966698108.Subproblem 1
x + -3.857142857 = 3.966698108 Simplifying x + -3.857142857 = 3.966698108 Reorder the terms: -3.857142857 + x = 3.966698108 Solving -3.857142857 + x = 3.966698108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.857142857' to each side of the equation. -3.857142857 + 3.857142857 + x = 3.966698108 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + x = 3.966698108 + 3.857142857 x = 3.966698108 + 3.857142857 Combine like terms: 3.966698108 + 3.857142857 = 7.823840965 x = 7.823840965 Simplifying x = 7.823840965Subproblem 2
x + -3.857142857 = -3.966698108 Simplifying x + -3.857142857 = -3.966698108 Reorder the terms: -3.857142857 + x = -3.966698108 Solving -3.857142857 + x = -3.966698108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.857142857' to each side of the equation. -3.857142857 + 3.857142857 + x = -3.966698108 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + x = -3.966698108 + 3.857142857 x = -3.966698108 + 3.857142857 Combine like terms: -3.966698108 + 3.857142857 = -0.109555251 x = -0.109555251 Simplifying x = -0.109555251Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.823840965, -0.109555251}
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