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Simplifying 40 = -0.01x2 + 0.5x + 2 Reorder the terms: 40 = 2 + 0.5x + -0.01x2 Solving 40 = 2 + 0.5x + -0.01x2 Solving for variable 'x'. Combine like terms: 40 + -2 = 38 38 + -0.5x + 0.01x2 = 2 + 0.5x + -0.01x2 + -2 + -0.5x + 0.01x2 Reorder the terms: 38 + -0.5x + 0.01x2 = 2 + -2 + 0.5x + -0.5x + -0.01x2 + 0.01x2 Combine like terms: 2 + -2 = 0 38 + -0.5x + 0.01x2 = 0 + 0.5x + -0.5x + -0.01x2 + 0.01x2 38 + -0.5x + 0.01x2 = 0.5x + -0.5x + -0.01x2 + 0.01x2 Combine like terms: 0.5x + -0.5x = 0.0 38 + -0.5x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 38 + -0.5x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 38 + -0.5x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 3800 + -50x + x2 = 0 Move the constant term to the right: Add '-3800' to each side of the equation. 3800 + -50x + -3800 + x2 = 0 + -3800 Reorder the terms: 3800 + -3800 + -50x + x2 = 0 + -3800 Combine like terms: 3800 + -3800 = 0 0 + -50x + x2 = 0 + -3800 -50x + x2 = 0 + -3800 Combine like terms: 0 + -3800 = -3800 -50x + x2 = -3800 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -3800 + 625 Reorder the terms: 625 + -50x + x2 = -3800 + 625 Combine like terms: -3800 + 625 = -3175 625 + -50x + x2 = -3175 Factor a perfect square on the left side: (x + -25)(x + -25) = -3175 Can't calculate square root of the right side. The solution to this equation could not be determined.
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