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Simplifying 0 = 0.25x2 + 5x + 52 Reorder the terms: 0 = 52 + 5x + 0.25x2 Solving 0 = 52 + 5x + 0.25x2 Solving for variable 'x'. Combine like terms: 0 + -52 = -52 -52 + -5x + -0.25x2 = 52 + 5x + 0.25x2 + -52 + -5x + -0.25x2 Reorder the terms: -52 + -5x + -0.25x2 = 52 + -52 + 5x + -5x + 0.25x2 + -0.25x2 Combine like terms: 52 + -52 = 0 -52 + -5x + -0.25x2 = 0 + 5x + -5x + 0.25x2 + -0.25x2 -52 + -5x + -0.25x2 = 5x + -5x + 0.25x2 + -0.25x2 Combine like terms: 5x + -5x = 0 -52 + -5x + -0.25x2 = 0 + 0.25x2 + -0.25x2 -52 + -5x + -0.25x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 -52 + -5x + -0.25x2 = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 208 + 20x + x2 = 0 Move the constant term to the right: Add '-208' to each side of the equation. 208 + 20x + -208 + x2 = 0 + -208 Reorder the terms: 208 + -208 + 20x + x2 = 0 + -208 Combine like terms: 208 + -208 = 0 0 + 20x + x2 = 0 + -208 20x + x2 = 0 + -208 Combine like terms: 0 + -208 = -208 20x + x2 = -208 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 = -208 + 100 Reorder the terms: 100 + 20x + x2 = -208 + 100 Combine like terms: -208 + 100 = -108 100 + 20x + x2 = -108 Factor a perfect square on the left side: (x + 10)(x + 10) = -108 Can't calculate square root of the right side. The solution to this equation could not be determined.
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