Solve for t square root of 2t-5-3=3

$\sqrt{2 t - 5} - 3 = 3$

Step 1

Move all terms not containing $\sqrt{2 t - 5}$ to the right side of the equation.

Add $3$ to both sides of the equation.

$\sqrt{2 t - 5} = 3 + 3$

Add $3$ and $3$ .

$\sqrt{2 t - 5} = 6$

Step 2

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

${\sqrt{2 t - 5}}^{2} = 6^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 t - 5}$ as ${(2 t - 5)}^{\frac{1}{2}}$ .

${({(2 t - 5)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${({(2 t - 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 t - 5)}^{\frac{1}{2}})}^{2}$ .

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

${(2 t - 5)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 t - 5)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(2 t - 5)}^{1} = 6^{2}$

Simplify.

$2 t - 5 = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$2 t - 5 = 36$

Step 4

Solve for $t$ .

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

Add $5$ to both sides of the equation.

$2 t = 36 + 5$

Add $36$ and $5$ .

$2 t = 41$

Divide each term in $2 t = 41$ by $2$ and simplify.

Divide each term in $2 t = 41$ by $2$ .

$\frac{2 t}{2} = \frac{41}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 t}{2} = \frac{41}{2}$

Divide $t$ by $1$ .

$t = \frac{41}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{41}{2}$

Decimal Form:

$t = 20.5$

Mixed Number Form:

$t = 20 \frac{1}{2}$

Solve for t square root of 2t-5-3=3

Related Questions

Support LCMGCF.com by disabling your adblocker.