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2 Solve the equation (x-3)/(16)=(4x)/(x-3).

22 Solve the equation x−316=4xx−3 \frac{x-3}{16}=\frac{4 x}{x-3} .

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Full solution

Q. 22 Solve the equation x−316=4xx−3 \frac{x-3}{16}=\frac{4 x}{x-3} .
  1. Cross Multiply: Cross multiply to get rid of the fractions: x\(-3)(x−3-3) = 1616(44x)\
  2. Expand Left Side: Expand the left side using the FOIL method: x2−3x−3x+9=64xx^2 - 3x - 3x + 9 = 64x.
  3. Combine Like Terms: Combine like terms on the left side: x2−6x+9=64xx^2 - 6x + 9 = 64x.
  4. Subtract 64x64x: Subtract 64x64x from both sides to get all xx terms on one side: x2−70x+9=0x^2 - 70x + 9 = 0.
  5. Use Quadratic Formula: Try to factor the quadratic, but it doesn't factor nicely. So, use the quadratic formula: x=−(−70)±(−70)2−4(1)(9)2×1x = \frac{-(-70) \pm \sqrt{(-70)^2 - 4(1)(9)}}{2 \times 1}.
  6. Simplify Formula: Simplify inside the square root and the rest of the formula: x=70±4900−362x = \frac{70 \pm \sqrt{4900 - 36}}{2}.
  7. Further Simplify: Further simplify the square root: x=70±48642x = \frac{70 \pm \sqrt{4864}}{2}.
  8. Calculate Square Root: Calculate the square root: x=70±702x = \frac{\sqrt{70} \pm \sqrt{70}}{2}.

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