Solve for x (2x-3)^(1/2)+2=2

${(2 x - 3)}^{\frac{1}{2}} + 2 = 2$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

${(2 x - 3)}^{\frac{1}{2}} = 2 - 2$

Subtract $2$ from $2$ .

${(2 x - 3)}^{\frac{1}{2}} = 0$

Step 2

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${({(2 x - 3)}^{\frac{1}{2}})}^{2} = 0^{2}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${({(2 x - 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x - 3)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(2 x - 3)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x - 3)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

${(2 x - 3)}^{1} = 0^{2}$

Simplify.

$2 x - 3 = 0^{2}$

Simplify the right side.

Raising $0$ to any positive power yields $0$ .

$2 x - 3 = 0$

Step 4

Solve for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$

Solve for x (2x-3)^(1/2)+2=2

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