Solved on Nov 08, 2023

Find the solutions to the equation $\sqrt{2x-1}-2=0$ .

STEP 1

Assumptions1. We are solving the equation $\sqrt{x -1} - =0$ for real number solutions. . The square root function is defined for non-negative real numbers.

STEP 2

First, we need to isolate the square root term. We can do this by adding2 to both sides of the equation.
$\sqrt{2x -1} -2 +2 =0 +2$

STEP 3

implify the equation.
$\sqrt{2x -1} =2$

STEP 4

Now, we need to eliminate the square root. We can do this by squaring both sides of the equation.
$(\sqrt{2x -1})^2 =2^2$

STEP 5

implify the equation.
$2x -1 =4$

STEP 6

Next, we need to isolate the variable $x$ . We can do this by adding1 to both sides of the equation.
$2x -1 +1 =4 +1$

STEP 7

implify the equation.
$2x =5$

STEP 8

Finally, we can solve for $x$ by dividing both sides of the equation by2.
$x = \frac{5}{2}$ So, the solution to the equation $\sqrt{2x -1} -2 =0$ is $x = \frac{5}{2}$ .

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Find the solutions to the equation $\sqrt{2x-1}-2=0$ .

STEP 1

Assumptions1. We are solving the equation $\sqrt{x -1} - =0$ for real number solutions. . The square root function is defined for non-negative real numbers.

STEP 2

First, we need to isolate the square root term. We can do this by adding2 to both sides of the equation.
$\sqrt{2x -1} -2 +2 =0 +2$

STEP 3

implify the equation.
$\sqrt{2x -1} =2$

STEP 4

Now, we need to eliminate the square root. We can do this by squaring both sides of the equation.
$(\sqrt{2x -1})^2 =2^2$

STEP 5

implify the equation.
$2x -1 =4$

STEP 6

Next, we need to isolate the variable $x$ . We can do this by adding1 to both sides of the equation.
$2x -1 +1 =4 +1$

STEP 7

implify the equation.
$2x =5$

STEP 8

Finally, we can solve for $x$ by dividing both sides of the equation by2.
$x = \frac{5}{2}$ So, the solution to the equation $\sqrt{2x -1} -2 =0$ is $x = \frac{5}{2}$ .

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Find the solutions to the equation 2x−1−2=0\sqrt{2x-1}-2=02x−1​−2=0.

STEP 1

Assumptions1. We are solving the equation x−1−=0\sqrt{x -1} - =0x−1​−=0 for real number solutions. . The square root function is defined for non-negative real numbers.

STEP 2

First, we need to isolate the square root term. We can do this by adding2 to both sides of the equation.2x−1−2+2=0+2\sqrt{2x -1} -2 +2 =0 +22x−1​−2+2=0+2

STEP 3

implify the equation.2x−1=2\sqrt{2x -1} =22x−1​=2

STEP 4

Now, we need to eliminate the square root. We can do this by squaring both sides of the equation.(2x−1)2=22(\sqrt{2x -1})^2 =2^2(2x−1​)2=22

STEP 5

implify the equation.2x−1=42x -1 =42x−1=4

STEP 6

Next, we need to isolate the variable xxx. We can do this by adding1 to both sides of the equation.2x−1+1=4+12x -1 +1 =4 +12x−1+1=4+1

STEP 7

implify the equation.2x=52x =52x=5

STEP 8

Finally, we can solve for xxx by dividing both sides of the equation by2.x=52x = \frac{5}{2}x=25​So, the solution to the equation 2x−1−2=0\sqrt{2x -1} -2 =02x−1​−2=0 is x=52x = \frac{5}{2}x=25​.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the solutions to the equation $\sqrt{2x-1}-2=0$ .

Assumptions1. We are solving the equation $\sqrt{x -1} - =0$ for real number solutions. . The square root function is defined for non-negative real numbers.

First, we need to isolate the square root term. We can do this by adding2 to both sides of the equation.
$\sqrt{2x -1} -2 +2 =0 +2$

implify the equation.
$\sqrt{2x -1} =2$

Now, we need to eliminate the square root. We can do this by squaring both sides of the equation.
$(\sqrt{2x -1})^2 =2^2$

implify the equation.
$2x -1 =4$

Next, we need to isolate the variable $x$ . We can do this by adding1 to both sides of the equation.
$2x -1 +1 =4 +1$

implify the equation.
$2x =5$

Finally, we can solve for $x$ by dividing both sides of the equation by2.
$x = \frac{5}{2}$ So, the solution to the equation $\sqrt{2x -1} -2 =0$ is $x = \frac{5}{2}$ .