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Simplifying 0 = 6x2 + 97x + 210 Reorder the terms: 0 = 210 + 97x + 6x2 Solving 0 = 210 + 97x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -210 = -210 -210 + -97x + -6x2 = 210 + 97x + 6x2 + -210 + -97x + -6x2 Reorder the terms: -210 + -97x + -6x2 = 210 + -210 + 97x + -97x + 6x2 + -6x2 Combine like terms: 210 + -210 = 0 -210 + -97x + -6x2 = 0 + 97x + -97x + 6x2 + -6x2 -210 + -97x + -6x2 = 97x + -97x + 6x2 + -6x2 Combine like terms: 97x + -97x = 0 -210 + -97x + -6x2 = 0 + 6x2 + -6x2 -210 + -97x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -210 + -97x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(210 + 97x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(210 + 97x + 6x2)' equal to zero and attempt to solve: Simplifying 210 + 97x + 6x2 = 0 Solving 210 + 97x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 35 + 16.16666667x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + 16.16666667x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 16.16666667x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 16.16666667x + x2 = 0 + -35 16.16666667x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 16.16666667x + x2 = -35 The x term is 16.16666667x. Take half its coefficient (8.083333335). Square it (65.34027780) and add it to both sides. Add '65.34027780' to each side of the equation. 16.16666667x + 65.34027780 + x2 = -35 + 65.34027780 Reorder the terms: 65.34027780 + 16.16666667x + x2 = -35 + 65.34027780 Combine like terms: -35 + 65.34027780 = 30.3402778 65.34027780 + 16.16666667x + x2 = 30.3402778 Factor a perfect square on the left side: (x + 8.083333335)(x + 8.083333335) = 30.3402778 Calculate the square root of the right side: 5.508200959 Break this problem into two subproblems by setting (x + 8.083333335) equal to 5.508200959 and -5.508200959.Subproblem 1
x + 8.083333335 = 5.508200959 Simplifying x + 8.083333335 = 5.508200959 Reorder the terms: 8.083333335 + x = 5.508200959 Solving 8.083333335 + x = 5.508200959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.083333335' to each side of the equation. 8.083333335 + -8.083333335 + x = 5.508200959 + -8.083333335 Combine like terms: 8.083333335 + -8.083333335 = 0.000000000 0.000000000 + x = 5.508200959 + -8.083333335 x = 5.508200959 + -8.083333335 Combine like terms: 5.508200959 + -8.083333335 = -2.575132376 x = -2.575132376 Simplifying x = -2.575132376Subproblem 2
x + 8.083333335 = -5.508200959 Simplifying x + 8.083333335 = -5.508200959 Reorder the terms: 8.083333335 + x = -5.508200959 Solving 8.083333335 + x = -5.508200959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.083333335' to each side of the equation. 8.083333335 + -8.083333335 + x = -5.508200959 + -8.083333335 Combine like terms: 8.083333335 + -8.083333335 = 0.000000000 0.000000000 + x = -5.508200959 + -8.083333335 x = -5.508200959 + -8.083333335 Combine like terms: -5.508200959 + -8.083333335 = -13.591534294 x = -13.591534294 Simplifying x = -13.591534294Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.575132376, -13.591534294}Solution
x = {-2.575132376, -13.591534294}
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