Solve by Factoring square root of 4x-3=7

$\sqrt{4 x - 3} = 7$

Step 1

Subtract $7$ from both sides of the equation.

$\sqrt{4 x - 3} - 7 = 0$

Step 2

Add $7$ to both sides of the equation.

$\sqrt{4 x - 3} = 7$

Step 3

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

${\sqrt{4 x - 3}}^{2} = 7^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x - 3}$ as ${(4 x - 3)}^{\frac{1}{2}}$ .

${({(4 x - 3)}^{\frac{1}{2}})}^{2} = 7^{2}$

Simplify the left side.

Simplify ${({(4 x - 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 x - 3)}^{\frac{1}{2}})}^{2}$ .

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

${(4 x - 3)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 x - 3)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Rewrite the expression.

${(4 x - 3)}^{1} = 7^{2}$

Simplify.

$4 x - 3 = 7^{2}$

Simplify the right side.

Raise $7$ to the power of $2$ .

$4 x - 3 = 49$

Step 5

Solve for $x$ .

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

Add $3$ to both sides of the equation.

$4 x = 49 + 3$

Add $49$ and $3$ .

$4 x = 52$

Divide each term in $4 x = 52$ by $4$ and simplify.

Divide each term in $4 x = 52$ by $4$ .

$\frac{4 x}{4} = \frac{52}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{52}{4}$

Divide $x$ by $1$ .

$x = \frac{52}{4}$

Simplify the right side.

Divide $52$ by $4$ .

$x = 13$

Solve by Factoring square root of 4x-3=7

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