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Simplifying x2 + -6x = x(8x + -2) + 6 Reorder the terms: -6x + x2 = x(8x + -2) + 6 Reorder the terms: -6x + x2 = x(-2 + 8x) + 6 -6x + x2 = (-2 * x + 8x * x) + 6 -6x + x2 = (-2x + 8x2) + 6 Reorder the terms: -6x + x2 = 6 + -2x + 8x2 Solving -6x + x2 = 6 + -2x + 8x2 Solving for variable 'x'. Reorder the terms: -6 + -6x + 2x + x2 + -8x2 = 6 + -2x + 8x2 + -6 + 2x + -8x2 Combine like terms: -6x + 2x = -4x -6 + -4x + x2 + -8x2 = 6 + -2x + 8x2 + -6 + 2x + -8x2 Combine like terms: x2 + -8x2 = -7x2 -6 + -4x + -7x2 = 6 + -2x + 8x2 + -6 + 2x + -8x2 Reorder the terms: -6 + -4x + -7x2 = 6 + -6 + -2x + 2x + 8x2 + -8x2 Combine like terms: 6 + -6 = 0 -6 + -4x + -7x2 = 0 + -2x + 2x + 8x2 + -8x2 -6 + -4x + -7x2 = -2x + 2x + 8x2 + -8x2 Combine like terms: -2x + 2x = 0 -6 + -4x + -7x2 = 0 + 8x2 + -8x2 -6 + -4x + -7x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -6 + -4x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 4x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 4x + 7x2)' equal to zero and attempt to solve: Simplifying 6 + 4x + 7x2 = 0 Solving 6 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 0.5714285714x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 0.5714285714x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + -0.8571428571 0.5714285714x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 0.5714285714x + x2 = -0.8571428571 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = -0.8571428571 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = -0.8571428571 + 0.08163265305 Combine like terms: -0.8571428571 + 0.08163265305 = -0.77551020405 0.08163265305 + 0.5714285714x + x2 = -0.77551020405 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = -0.77551020405 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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