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Simplifying 0 = 0.2x2 + 10x + 2500 Reorder the terms: 0 = 2500 + 10x + 0.2x2 Solving 0 = 2500 + 10x + 0.2x2 Solving for variable 'x'. Combine like terms: 0 + -2500 = -2500 -2500 + -10x + -0.2x2 = 2500 + 10x + 0.2x2 + -2500 + -10x + -0.2x2 Reorder the terms: -2500 + -10x + -0.2x2 = 2500 + -2500 + 10x + -10x + 0.2x2 + -0.2x2 Combine like terms: 2500 + -2500 = 0 -2500 + -10x + -0.2x2 = 0 + 10x + -10x + 0.2x2 + -0.2x2 -2500 + -10x + -0.2x2 = 10x + -10x + 0.2x2 + -0.2x2 Combine like terms: 10x + -10x = 0 -2500 + -10x + -0.2x2 = 0 + 0.2x2 + -0.2x2 -2500 + -10x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 -2500 + -10x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 12500 + 50x + x2 = 0 Move the constant term to the right: Add '-12500' to each side of the equation. 12500 + 50x + -12500 + x2 = 0 + -12500 Reorder the terms: 12500 + -12500 + 50x + x2 = 0 + -12500 Combine like terms: 12500 + -12500 = 0 0 + 50x + x2 = 0 + -12500 50x + x2 = 0 + -12500 Combine like terms: 0 + -12500 = -12500 50x + x2 = -12500 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 = -12500 + 625 Reorder the terms: 625 + 50x + x2 = -12500 + 625 Combine like terms: -12500 + 625 = -11875 625 + 50x + x2 = -11875 Factor a perfect square on the left side: (x + 25)(x + 25) = -11875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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