What is the answer to x^2+2x-15=2(x+5)sqrt(x) ?

The answer to x^2+2x-15=2(x+5)sqrt(x) is x=9

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x^2+2x-15=2(x+5)sqrt(x)

x^{2} + 2 x - 15 = 2 (x + 5) x

x = 9

Solution steps

x^{2} + 2 x - 15 = 2 (x + 5) x

Expand

2 (x + 5) x : 2 x x + 10 x

x^{2} + 2 x - 15 = 2 x x + 10 x

Factor

x^{2} + 2 x - 15 : (x - 3) (x + 5)

Factor

2 x x + 10 x : 2 x (x + 5)

(x - 3) (x + 5) = 2 x (x + 5)

Move

2 x (x + 5)

to the left side

(x - 3) (x + 5) - 2 x (x + 5) = 0

Factor

(x - 3) (x + 5) - 2 x (x + 5) : (5 + x) (- 3 + x - 2 x)

(5 + x) (- 3 + x - 2 x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5 + x = 0 or - 3 + x - 2 x = 0

Solve

5 + x = 0 : x = - 5

Solve

- 3 + x - 2 x = 0 : x = 9

x = - 5, x = 9

Verify Solutions:

x = - 5

False

, x = 9

True

The solution is

x = 9

3 x + 1 = 11

5 = 3 x - 2

12 - 4 x - x = 0

(x - 7)^{2} = (3)^{2}

23 = x - 11 - 5

What is the answer to x^2+2x-15=2(x+5)sqrt(x) ?
The answer to x^2+2x-15=2(x+5)sqrt(x) is x=9
Solve for x: x^2+2x-15=2(x+5)sqrt(x)
The solution is x=9