What is the answer to (sqrt(6x+21)+3)^2=(x-2)^2 ?

The answer to (sqrt(6x+21)+3)^2=(x-2)^2 is x=-2.89897…,x=15.74596…

Solve for x: (sqrt(6x+21)+3)^2=(x-2)^2

The solution is x=-2.89897…,x=15.74596…

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(6 x + 21 + 3)^{2} = (x - 2)^{2}

x = - 2.89897 \dots, x = 15.74596 \dots

Solution steps

(6 x + 21 + 3)^{2} = (x - 2)^{2}

Rewrite the equation with

6 x + 21 = u

and

x = \frac{u ^{2} - 21}{6}

(u + 3)^{2} = ((\frac{u ^{2} - 21}{6}) - 2)^{2}

Solve

(u + 3)^{2} = ((\frac{u ^{2} - 21}{6}) - 2)^{2} : u \approx 1.89897 \dots, u \approx - 4.74596 \dots, u \approx - 7.89897 \dots, u \approx 10.74596 \dots

u \approx 1.89897 \dots, u \approx - 4.74596 \dots, u \approx - 7.89897 \dots, u \approx 10.74596 \dots

Substitute back

u = 6 x + 21,

solve for

x

Solve

6 x + 21 = 1.89897 \dots : x = - 2.89897 \dots

Solve

6 x + 21 = - 4.74596 \dots :

No Solution for

x \in R

Solve

6 x + 21 = - 7.89897 \dots :

No Solution for

x \in R

Solve

6 x + 21 = 10.74596 \dots : x = 15.74596 \dots

x = - 2.89897 \dots, x = 15.74596 \dots

Verify Solutions:

x = - 2.89897 \dots

True

, x = 15.74596 \dots

True

The solutions are

x = - 2.89897 \dots, x = 15.74596 \dots

x + 3 = 9 - x

150 \cdot 15 = 12 j

0 = x + 1 - 2

\frac{1}{n} \cdot 100 = 5

7 x + 126 = 14

What is the answer to (sqrt(6x+21)+3)^2=(x-2)^2 ?
The answer to (sqrt(6x+21)+3)^2=(x-2)^2 is x=-2.89897…,x=15.74596…
Solve for x: (sqrt(6x+21)+3)^2=(x-2)^2
The solution is x=-2.89897…,x=15.74596…