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Simplifying 50 = 0.004x2 + -1x + 80 Reorder the terms: 50 = 80 + -1x + 0.004x2 Solving 50 = 80 + -1x + 0.004x2 Solving for variable 'x'. Combine like terms: 50 + -80 = -30 -30 + x + -0.004x2 = 80 + -1x + 0.004x2 + -80 + x + -0.004x2 Reorder the terms: -30 + x + -0.004x2 = 80 + -80 + -1x + x + 0.004x2 + -0.004x2 Combine like terms: 80 + -80 = 0 -30 + x + -0.004x2 = 0 + -1x + x + 0.004x2 + -0.004x2 -30 + x + -0.004x2 = -1x + x + 0.004x2 + -0.004x2 Combine like terms: -1x + x = 0 -30 + x + -0.004x2 = 0 + 0.004x2 + -0.004x2 -30 + x + -0.004x2 = 0.004x2 + -0.004x2 Combine like terms: 0.004x2 + -0.004x2 = 0.000 -30 + x + -0.004x2 = 0.000 Begin completing the square. Divide all terms by -0.004 the coefficient of the squared term: Divide each side by '-0.004'. 7500 + -250x + x2 = 0 Move the constant term to the right: Add '-7500' to each side of the equation. 7500 + -250x + -7500 + x2 = 0 + -7500 Reorder the terms: 7500 + -7500 + -250x + x2 = 0 + -7500 Combine like terms: 7500 + -7500 = 0 0 + -250x + x2 = 0 + -7500 -250x + x2 = 0 + -7500 Combine like terms: 0 + -7500 = -7500 -250x + x2 = -7500 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. -250x + 0.25 + x2 = -7500 + 0.25 Reorder the terms: 0.25 + -250x + x2 = -7500 + 0.25 Combine like terms: -7500 + 0.25 = -7499.75 0.25 + -250x + x2 = -7499.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -7499.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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