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Simplifying 0.75x + 0.05x(10 + -1x) = 0.10(117) 0.75x + (10 * 0.05x + -1x * 0.05x) = 0.10(117) 0.75x + (0.5x + -0.05x2) = 0.10(117) Combine like terms: 0.75x + 0.5x = 1.25x 1.25x + -0.05x2 = 0.10(117) Multiply 0.10 * 117 1.25x + -0.05x2 = 11.7 Solving 1.25x + -0.05x2 = 11.7 Solving for variable 'x'. Reorder the terms: -11.7 + 1.25x + -0.05x2 = 11.7 + -11.7 Combine like terms: 11.7 + -11.7 = 0.0 -11.7 + 1.25x + -0.05x2 = 0.0 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 234 + -25x + x2 = 0 Move the constant term to the right: Add '-234' to each side of the equation. 234 + -25x + -234 + x2 = 0 + -234 Reorder the terms: 234 + -234 + -25x + x2 = 0 + -234 Combine like terms: 234 + -234 = 0 0 + -25x + x2 = 0 + -234 -25x + x2 = 0 + -234 Combine like terms: 0 + -234 = -234 -25x + x2 = -234 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -234 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -234 + 156.25 Combine like terms: -234 + 156.25 = -77.75 156.25 + -25x + x2 = -77.75 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = -77.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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