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Simplifying 0 = 0.6x2 + 3x + 6 Reorder the terms: 0 = 6 + 3x + 0.6x2 Solving 0 = 6 + 3x + 0.6x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -3x + -0.6x2 = 6 + 3x + 0.6x2 + -6 + -3x + -0.6x2 Reorder the terms: -6 + -3x + -0.6x2 = 6 + -6 + 3x + -3x + 0.6x2 + -0.6x2 Combine like terms: 6 + -6 = 0 -6 + -3x + -0.6x2 = 0 + 3x + -3x + 0.6x2 + -0.6x2 -6 + -3x + -0.6x2 = 3x + -3x + 0.6x2 + -0.6x2 Combine like terms: 3x + -3x = 0 -6 + -3x + -0.6x2 = 0 + 0.6x2 + -0.6x2 -6 + -3x + -0.6x2 = 0.6x2 + -0.6x2 Combine like terms: 0.6x2 + -0.6x2 = 0.0 -6 + -3x + -0.6x2 = 0.0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. 10 + 5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 5x + x2 = 0 + -10 5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 5x + x2 = -10 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -10 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -10 + 6.25 Combine like terms: -10 + 6.25 = -3.75 6.25 + 5x + x2 = -3.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -3.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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