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Simplifying -1x2 + -1x + -2 = 6x2 Reorder the terms: -2 + -1x + -1x2 = 6x2 Solving -2 + -1x + -1x2 = 6x2 Solving for variable 'x'. Combine like terms: -1x2 + -6x2 = -7x2 -2 + -1x + -7x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -2 + -1x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + x + 7x2)' equal to zero and attempt to solve: Simplifying 2 + x + 7x2 = 0 Solving 2 + x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 0.1428571429x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 0.1428571429x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + -0.2857142857 0.1428571429x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 0.1428571429x + x2 = -0.2857142857 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1428571429x + 0.25 + x2 = -0.2857142857 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = -0.2857142857 + 0.25 Combine like terms: -0.2857142857 + 0.25 = -0.0357142857 0.25 + 0.1428571429x + x2 = -0.0357142857 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.0357142857 Can't calculate square root of the right side. 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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