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Make x the subject of the formula N = (-t) / sqrt(ax + bx)

Mathematics

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Step-by-step solution

13 steps

1.

  1. Start with the given equation.

    y=bxy = bx

  2. Divide both sides by bb.

    x=ybx = \frac{y}{b}

    x = \frac{y}{b}

    2.

  3. Start with the given equation.

    a=b−da = \sqrt{b - d}

  4. Square both sides.

    a2=b−da^{2} = b - d

  5. Add dd to both sides.

    b=a2+db = a^{2} + d

    b = a^{2} + d

    3.

  6. Start with the given equation.

    (p−q)(p−r)=x(p - q)(p - r) = x

  7. Expand the left side.

    p2−pr−pq+qr=xp^{2} - pr - pq + qr = x

  8. Rearrange into standard quadratic form.

    p2−(q+r)p+(qr−x)=0p^{2} - (q + r)p + (qr - x) = 0

  9. Apply the quadratic formula, where A=1A = 1, B=−(q+r)B = -(q + r), C=qr−xC = qr - x.

    p=(q+r)±(q+r)2−4(1)(qr−x)2p = \frac{(q + r) \pm \sqrt{(q + r)^{2} - 4(1)(qr - x)}}{2}

    p = \frac{(q + r) \pm \sqrt{(q + r)^{2} - 4(qr - x)}}{2}

    4.

  10. Start with the given equation.

    N=ax+bxN = \sqrt{ax + bx}

  11. Factor xx on the right side.

    N=x(a+b)N = \sqrt{x(a + b)}

  12. Square both sides.

    N2=x(a+b)N^{2} = x(a + b)

  13. Divide both sides by (a+b)(a + b).

    x=N2a+bx = \frac{N^{2}}{a + b}

    x = \frac{N^{2}}{a + b}

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