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Simplifying 0 = 0.5x2 + -1x + 40 Reorder the terms: 0 = 40 + -1x + 0.5x2 Solving 0 = 40 + -1x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + x + -0.5x2 = 40 + -1x + 0.5x2 + -40 + x + -0.5x2 Reorder the terms: -40 + x + -0.5x2 = 40 + -40 + -1x + x + 0.5x2 + -0.5x2 Combine like terms: 40 + -40 = 0 -40 + x + -0.5x2 = 0 + -1x + x + 0.5x2 + -0.5x2 -40 + x + -0.5x2 = -1x + x + 0.5x2 + -0.5x2 Combine like terms: -1x + x = 0 -40 + x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -40 + x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -40 + x + -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'. 80 + -2x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -2x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -2x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -2x + x2 = 0 + -80 -2x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -2x + x2 = -80 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. -2x + 0.25 + x2 = -80 + 0.25 Reorder the terms: 0.25 + -2x + x2 = -80 + 0.25 Combine like terms: -80 + 0.25 = -79.75 0.25 + -2x + x2 = -79.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -79.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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