What is the answer to 7-sqrt(X)=sqrt(5\sqrt{X-29)} ?

The answer to 7-sqrt(X)=sqrt(5\sqrt{X-29)} is X\approx 29.25635…

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7-sqrt(X)=sqrt(5\sqrt{X-29)}

7 - X = 5 X - 29

X \approx 29.25635 \dots

Solution steps

7 - X = 5 X - 29

Remove square roots

784 X^{3} + 76832 X^{2} + 1882384 X = X^{4} + 538 X^{3} + 78613 X^{2} + 1681788 X + 9771876

Move

X^{2}

to the right side

- 28 X X + 294 X - 1372 X + 2401 = 25 X - 725 - X^{2}

Move

294 X

to the right side

- 28 X X - 1372 X + 2401 = - X^{2} - 269 X - 725

Move

2401

to the right side

- 28 X X - 1372 X = - X^{2} - 269 X - 3126

Factor

- 28 X X - 1372 X : - 28 X (X + 49)

- 28 X (X + 49) = - X^{2} - 269 X - 3126

Solve

784 X^{3} + 76832 X^{2} + 1882384 X = X^{4} + 538 X^{3} + 78613 X^{2} + 1681788 X + 9771876 : X \approx 29.25635 \dots, X \approx 241.36952 \dots

X \approx 29.25635 \dots, X \approx 241.36952 \dots

Verify Solutions:

X \approx 29.25635 \dots

True

, X \approx 241.36952 \dots

False

The solution is

X \approx 29.25635 \dots

7 - x - 19 + x = - 2

2 x + 5 - 3 = 0

x^{\frac{1}{2}} = \frac{1}{3}

- 2 = x^{\frac{- 1}{2}}

What is the answer to 7-sqrt(X)=sqrt(5\sqrt{X-29)} ?
The answer to 7-sqrt(X)=sqrt(5\sqrt{X-29)} is X\approx 29.25635…
Solve for X: 7-sqrt(X)=sqrt(5\sqrt{X-29)}
The solution is X\approx 29.25635…