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Simplifying 6x2 + -37x + -21 = 0 Reorder the terms: -21 + -37x + 6x2 = 0 Solving -21 + -37x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.5 + -6.166666667x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -6.166666667x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -6.166666667x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -6.166666667x + x2 = 0 + 3.5 -6.166666667x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -6.166666667x + x2 = 3.5 The x term is -6.166666667x. Take half its coefficient (-3.083333334). Square it (9.506944449) and add it to both sides. Add '9.506944449' to each side of the equation. -6.166666667x + 9.506944449 + x2 = 3.5 + 9.506944449 Reorder the terms: 9.506944449 + -6.166666667x + x2 = 3.5 + 9.506944449 Combine like terms: 3.5 + 9.506944449 = 13.006944449 9.506944449 + -6.166666667x + x2 = 13.006944449 Factor a perfect square on the left side: (x + -3.083333334)(x + -3.083333334) = 13.006944449 Calculate the square root of the right side: 3.606514169 Break this problem into two subproblems by setting (x + -3.083333334) equal to 3.606514169 and -3.606514169.Subproblem 1
x + -3.083333334 = 3.606514169 Simplifying x + -3.083333334 = 3.606514169 Reorder the terms: -3.083333334 + x = 3.606514169 Solving -3.083333334 + x = 3.606514169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.083333334' to each side of the equation. -3.083333334 + 3.083333334 + x = 3.606514169 + 3.083333334 Combine like terms: -3.083333334 + 3.083333334 = 0.000000000 0.000000000 + x = 3.606514169 + 3.083333334 x = 3.606514169 + 3.083333334 Combine like terms: 3.606514169 + 3.083333334 = 6.689847503 x = 6.689847503 Simplifying x = 6.689847503Subproblem 2
x + -3.083333334 = -3.606514169 Simplifying x + -3.083333334 = -3.606514169 Reorder the terms: -3.083333334 + x = -3.606514169 Solving -3.083333334 + x = -3.606514169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.083333334' to each side of the equation. -3.083333334 + 3.083333334 + x = -3.606514169 + 3.083333334 Combine like terms: -3.083333334 + 3.083333334 = 0.000000000 0.000000000 + x = -3.606514169 + 3.083333334 x = -3.606514169 + 3.083333334 Combine like terms: -3.606514169 + 3.083333334 = -0.523180835 x = -0.523180835 Simplifying x = -0.523180835Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.689847503, -0.523180835}
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