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Simplifying 6x2 + 108x + -592 = 0 Reorder the terms: -592 + 108x + 6x2 = 0 Solving -592 + 108x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-296 + 54x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-296 + 54x + 3x2)' equal to zero and attempt to solve: Simplifying -296 + 54x + 3x2 = 0 Solving -296 + 54x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -98.66666667 + 18x + x2 = 0 Move the constant term to the right: Add '98.66666667' to each side of the equation. -98.66666667 + 18x + 98.66666667 + x2 = 0 + 98.66666667 Reorder the terms: -98.66666667 + 98.66666667 + 18x + x2 = 0 + 98.66666667 Combine like terms: -98.66666667 + 98.66666667 = 0.00000000 0.00000000 + 18x + x2 = 0 + 98.66666667 18x + x2 = 0 + 98.66666667 Combine like terms: 0 + 98.66666667 = 98.66666667 18x + x2 = 98.66666667 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 98.66666667 + 81 Reorder the terms: 81 + 18x + x2 = 98.66666667 + 81 Combine like terms: 98.66666667 + 81 = 179.66666667 81 + 18x + x2 = 179.66666667 Factor a perfect square on the left side: (x + 9)(x + 9) = 179.66666667 Calculate the square root of the right side: 13.403979509 Break this problem into two subproblems by setting (x + 9) equal to 13.403979509 and -13.403979509.Subproblem 1
x + 9 = 13.403979509 Simplifying x + 9 = 13.403979509 Reorder the terms: 9 + x = 13.403979509 Solving 9 + x = 13.403979509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 13.403979509 + -9 Combine like terms: 9 + -9 = 0 0 + x = 13.403979509 + -9 x = 13.403979509 + -9 Combine like terms: 13.403979509 + -9 = 4.403979509 x = 4.403979509 Simplifying x = 4.403979509Subproblem 2
x + 9 = -13.403979509 Simplifying x + 9 = -13.403979509 Reorder the terms: 9 + x = -13.403979509 Solving 9 + x = -13.403979509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -13.403979509 + -9 Combine like terms: 9 + -9 = 0 0 + x = -13.403979509 + -9 x = -13.403979509 + -9 Combine like terms: -13.403979509 + -9 = -22.403979509 x = -22.403979509 Simplifying x = -22.403979509Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.403979509, -22.403979509}Solution
x = {4.403979509, -22.403979509}
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