What is the answer to sqrt(x+3)+sqrt(x-5)=7x-x^2-2 ?

The answer to sqrt(x+3)+sqrt(x-5)=7x-x^2-2 is x=6

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sqrt(x+3)+sqrt(x-5)=7x-x^2-2

x + 3 + x - 5 = 7 x - x^{2} - 2

x = 6

Solution steps

x + 3 + x - 5 = 7 x - x^{2} - 2

Rewrite the equation with

x + 3 = u

and

x = u^{2} - 3

u + (u^{2} - 3) - 5 = 7 (u^{2} - 3) - (u^{2} - 3)^{2} - 2

Solve

u + (u^{2} - 3) - 5 = 7 (u^{2} - 3) - (u^{2} - 3)^{2} - 2 : u = 3, u \approx - 3.15671 \dots

u = 3, u \approx - 3.15671 \dots

Substitute back

u = x + 3,

solve for

x

Solve

x + 3 = 3 : x = 6

Solve

x + 3 = - 3.15671 \dots :

No Solution for

x \in R

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

x + 4 = 2 x - 1

2 x + 10 - 1 = x

- 2 + 3 x + 2 = x

x + 1 = x - 5

2 x + 9 - x + 1 = x + 4

What is the answer to sqrt(x+3)+sqrt(x-5)=7x-x^2-2 ?
The answer to sqrt(x+3)+sqrt(x-5)=7x-x^2-2 is x=6
Solve for x: sqrt(x+3)+sqrt(x-5)=7x-x^2-2
The solution is x=6