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Simplifying 11 = 0.5x2 + 10x + 7000 Reorder the terms: 11 = 7000 + 10x + 0.5x2 Solving 11 = 7000 + 10x + 0.5x2 Solving for variable 'x'. Combine like terms: 11 + -7000 = -6989 -6989 + -10x + -0.5x2 = 7000 + 10x + 0.5x2 + -7000 + -10x + -0.5x2 Reorder the terms: -6989 + -10x + -0.5x2 = 7000 + -7000 + 10x + -10x + 0.5x2 + -0.5x2 Combine like terms: 7000 + -7000 = 0 -6989 + -10x + -0.5x2 = 0 + 10x + -10x + 0.5x2 + -0.5x2 -6989 + -10x + -0.5x2 = 10x + -10x + 0.5x2 + -0.5x2 Combine like terms: 10x + -10x = 0 -6989 + -10x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -6989 + -10x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -6989 + -10x + -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'. 13978 + 20x + x2 = 0 Move the constant term to the right: Add '-13978' to each side of the equation. 13978 + 20x + -13978 + x2 = 0 + -13978 Reorder the terms: 13978 + -13978 + 20x + x2 = 0 + -13978 Combine like terms: 13978 + -13978 = 0 0 + 20x + x2 = 0 + -13978 20x + x2 = 0 + -13978 Combine like terms: 0 + -13978 = -13978 20x + x2 = -13978 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -13978 + 100 Reorder the terms: 100 + 20x + x2 = -13978 + 100 Combine like terms: -13978 + 100 = -13878 100 + 20x + x2 = -13878 Factor a perfect square on the left side: (x + 10)(x + 10) = -13878 Can't calculate square root of the right side. The solution to this equation could not be determined.
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