What is the answer to x^2+24x+sqrt(x^2+24x)=30 ?

The answer to x^2+24x+sqrt(x^2+24x)=30 is x=1,x=-25

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x^2+24x+sqrt(x^2+24x)=30

x^{2} + 24 x + x^{2} + 24 x = 30

x = 1, x = - 25

Solution steps

x^{2} + 24 x + x^{2} + 24 x = 30

Remove square roots

x^{2} + 24 x = x^{4} + 48 x^{3} + 516 x^{2} - 1440 x + 900

Solve

x^{2} + 24 x = x^{4} + 48 x^{3} + 516 x^{2} - 1440 x + 900 : x = 1, x = - 25, x = 6 (5 - 2), x = - 6 (2 + 5)

x = 1, x = - 25, x = 6 (5 - 2), x = - 6 (2 + 5)

Verify Solutions:

x = 1

True

, x = - 25

True

, x = 6 (5 - 2)

False

, x = - 6 (2 + 5)

False

The solutions are

x = 1, x = - 25

\frac{x}{2} = 1

x^{2} + 3 x + 6 - 3 x = x^{2} + 4

3.7 \cdot x^{\frac{1}{2}} - 2.2 = 0

10 y + 14 = 7 y + 1 + 2

2 = x - 4

What is the answer to x^2+24x+sqrt(x^2+24x)=30 ?
The answer to x^2+24x+sqrt(x^2+24x)=30 is x=1,x=-25
Solve for x: x^2+24x+sqrt(x^2+24x)=30
The solution is x=1,x=-25