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Simplifying 0 = 4x2 + -41x + 117 Reorder the terms: 0 = 117 + -41x + 4x2 Solving 0 = 117 + -41x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -117 = -117 -117 + 41x + -4x2 = 117 + -41x + 4x2 + -117 + 41x + -4x2 Reorder the terms: -117 + 41x + -4x2 = 117 + -117 + -41x + 41x + 4x2 + -4x2 Combine like terms: 117 + -117 = 0 -117 + 41x + -4x2 = 0 + -41x + 41x + 4x2 + -4x2 -117 + 41x + -4x2 = -41x + 41x + 4x2 + -4x2 Combine like terms: -41x + 41x = 0 -117 + 41x + -4x2 = 0 + 4x2 + -4x2 -117 + 41x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -117 + 41x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 29.25 + -10.25x + x2 = 0 Move the constant term to the right: Add '-29.25' to each side of the equation. 29.25 + -10.25x + -29.25 + x2 = 0 + -29.25 Reorder the terms: 29.25 + -29.25 + -10.25x + x2 = 0 + -29.25 Combine like terms: 29.25 + -29.25 = 0.00 0.00 + -10.25x + x2 = 0 + -29.25 -10.25x + x2 = 0 + -29.25 Combine like terms: 0 + -29.25 = -29.25 -10.25x + x2 = -29.25 The x term is -10.25x. Take half its coefficient (-5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. -10.25x + 26.265625 + x2 = -29.25 + 26.265625 Reorder the terms: 26.265625 + -10.25x + x2 = -29.25 + 26.265625 Combine like terms: -29.25 + 26.265625 = -2.984375 26.265625 + -10.25x + x2 = -2.984375 Factor a perfect square on the left side: (x + -5.125)(x + -5.125) = -2.984375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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