Question

√2x+1=√x+4

Answer 1

Start by taking the square root of both sides.

Answer 2

Since x√ is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.

x√+4=2x−−√+1

Since 4 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4 from both sides.

x√=−4+2x−−√+1

Add 1 to −4 to get −3.

x√=−3+2x−−√

To remove the radical on the left-hand side of the equation, square both sides of the equation.

(x√)2=(−3+2x−−√)2

Simplify the left-hand side of the equation.

x=(−3+2x−−√)2

Simplify the right-hand side of the equation.

x=9−62x−−√+2x

Since the radical is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.

9−62x−−√+2x=x

Move all terms not containing 2x−−√ to the right-hand side of the equation.

−62x−−√=−9−2x+x

Simplify the right-hand side of the equation.

−62x−−√=−x−9

To remove the radical on the left-hand side of the equation, square both sides of the equation.

(−62x−−√)2=(−x−9)2

Simplify the left-hand side of the equation.

(−6)2(2x)=(−x−9)2

Simplify the right-hand side of the equation.

(−6)2(2x)=x2+18x+81

Squaring an expression is the same as multiplying the expression by itself 2 times.

(−6)(−6)(2x)=x2+18x+81

Multiply to simplify the expression (−6)(−6).

36(2x)=x2+18x+81

Multiply 36 by each term inside the parentheses.

72x=x2+18x+81

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.

x2+18x+81=72x

Since 72x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 72x from both sides.

x2+18x+81−72x=0

Since 18x and −72x are like terms, add −72x to 18x to get −54x.

x2−54x+81=0

Use the standard form of the quadratic (ax2+bx+c) to find a,b, and c for this quadratic.

a=1,b=−54,c=81

Use the quadratic formula to find the solutions.

x=−b ± b2−4ac−−−−−−−√ 2a

Substitute in the values of a=1,b=−54, and c=81.

x=−(−54) ± (−54)2−4(1)(81)−−−−−−−−−−−−−−−√ 2(1)

Multiply −1 by each term inside the parentheses.

x=54 ± (−54)2−4(1)(81)−−−−−−−−−−−−−−−√ 2(1)

Simplify the discriminant.

x=54 ± 36 2√ 2(1)

Simplify the denominator.

x=12(54±362√)

Solve the

x=27+182√

Solve the − portion of ±,(54−36 2√ )(2).

x=27−182√

The final answer is the combination of both solutions.

x=27+182√,27−182√

Verify each of the solutions by substituting them back into the original equation 2x−−√+1=x√+4 and solving. In this case, the solution (27−182√) was proven to be invalid during this process.

x=27+182√
x≈52.455844122716

Answer 3

is this multiple choice?

Answer 4

yes
A) 3
B) 1/3
C) -3
d) 1

Answer 5

\(\sqrt{2x + 1} = \sqrt{x + 4}\)

Start by squaring both sides to get:
2x + 1 = x + 4

Then solve for x

Answer 6

thank you!!

Answer 7

wait i am lost i did that and I got 1x=3???? what do i do next

Answer 8

1x means the same thing as x. So you have x=3

Answer 9

At that point, you can plug it in and check it.

Answer 10

okay thanks. sorry i am not that good at math

Answer 11

\(1 \times 2 = 2\)
\(1 \times 3 = 3\)
\(1 \times 4 = 4\)
\(1 \times 5 = 5\)
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\(1 \times x = x\)