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Simplifying 0 = 0.5x2 + -6x + 21 Reorder the terms: 0 = 21 + -6x + 0.5x2 Solving 0 = 21 + -6x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + -21 = -21 -21 + 6x + -0.5x2 = 21 + -6x + 0.5x2 + -21 + 6x + -0.5x2 Reorder the terms: -21 + 6x + -0.5x2 = 21 + -21 + -6x + 6x + 0.5x2 + -0.5x2 Combine like terms: 21 + -21 = 0 -21 + 6x + -0.5x2 = 0 + -6x + 6x + 0.5x2 + -0.5x2 -21 + 6x + -0.5x2 = -6x + 6x + 0.5x2 + -0.5x2 Combine like terms: -6x + 6x = 0 -21 + 6x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -21 + 6x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -21 + 6x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 42 + -12x + x2 = 0 Move the constant term to the right: Add '-42' to each side of the equation. 42 + -12x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -12x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -12x + x2 = 0 + -42 -12x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -12x + x2 = -42 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -42 + 36 Reorder the terms: 36 + -12x + x2 = -42 + 36 Combine like terms: -42 + 36 = -6 36 + -12x + x2 = -6 Factor a perfect square on the left side: (x + -6)(x + -6) = -6 Can't calculate square root of the right side. The solution to this equation could not be determined.
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