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Simplifying 2x2 + x + -21 = 8x2 Reorder the terms: -21 + x + 2x2 = 8x2 Solving -21 + x + 2x2 = 8x2 Solving for variable 'x'. Combine like terms: 2x2 + -8x2 = -6x2 -21 + x + -6x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -21 + x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 3.5 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -0.1666666667x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -0.1666666667x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -0.1666666667x + x2 = 0 + -3.5 -0.1666666667x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -0.1666666667x + x2 = -3.5 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. -0.1666666667x + 0.25 + x2 = -3.5 + 0.25 Reorder the terms: 0.25 + -0.1666666667x + x2 = -3.5 + 0.25 Combine like terms: -3.5 + 0.25 = -3.25 0.25 + -0.1666666667x + x2 = -3.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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