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Simplifying 0 = 0.1x2 + 8x + 3050 Reorder the terms: 0 = 3050 + 8x + 0.1x2 Solving 0 = 3050 + 8x + 0.1x2 Solving for variable 'x'. Combine like terms: 0 + -3050 = -3050 -3050 + -8x + -0.1x2 = 3050 + 8x + 0.1x2 + -3050 + -8x + -0.1x2 Reorder the terms: -3050 + -8x + -0.1x2 = 3050 + -3050 + 8x + -8x + 0.1x2 + -0.1x2 Combine like terms: 3050 + -3050 = 0 -3050 + -8x + -0.1x2 = 0 + 8x + -8x + 0.1x2 + -0.1x2 -3050 + -8x + -0.1x2 = 8x + -8x + 0.1x2 + -0.1x2 Combine like terms: 8x + -8x = 0 -3050 + -8x + -0.1x2 = 0 + 0.1x2 + -0.1x2 -3050 + -8x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -3050 + -8x + -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'. 30500 + 80x + x2 = 0 Move the constant term to the right: Add '-30500' to each side of the equation. 30500 + 80x + -30500 + x2 = 0 + -30500 Reorder the terms: 30500 + -30500 + 80x + x2 = 0 + -30500 Combine like terms: 30500 + -30500 = 0 0 + 80x + x2 = 0 + -30500 80x + x2 = 0 + -30500 Combine like terms: 0 + -30500 = -30500 80x + x2 = -30500 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = -30500 + 1600 Reorder the terms: 1600 + 80x + x2 = -30500 + 1600 Combine like terms: -30500 + 1600 = -28900 1600 + 80x + x2 = -28900 Factor a perfect square on the left side: (x + 40)(x + 40) = -28900 Can't calculate square root of the right side. The solution to this equation could not be determined.
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