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Simplifying 400 = 5(x) + -0.1(x2) Solving 400 = 5x + -0.1x2 Solving for variable 'x'. Reorder the terms: 400 + -5x + 0.1x2 = 5x + -5x + -0.1x2 + 0.1x2 Combine like terms: 5x + -5x = 0 400 + -5x + 0.1x2 = 0 + -0.1x2 + 0.1x2 400 + -5x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 400 + -5x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 4000 + -50x + x2 = 0 Move the constant term to the right: Add '-4000' to each side of the equation. 4000 + -50x + -4000 + x2 = 0 + -4000 Reorder the terms: 4000 + -4000 + -50x + x2 = 0 + -4000 Combine like terms: 4000 + -4000 = 0 0 + -50x + x2 = 0 + -4000 -50x + x2 = 0 + -4000 Combine like terms: 0 + -4000 = -4000 -50x + x2 = -4000 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 = -4000 + 625 Reorder the terms: 625 + -50x + x2 = -4000 + 625 Combine like terms: -4000 + 625 = -3375 625 + -50x + x2 = -3375 Factor a perfect square on the left side: (x + -25)(x + -25) = -3375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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