Solve for d square root of 7d+1-4=11

$\sqrt{7 d + 1} - 4 = 11$

Step 1

Move all terms not containing $\sqrt{7 d + 1}$ to the right side of the equation.

Add $4$ to both sides of the equation.

$\sqrt{7 d + 1} = 11 + 4$

Add $11$ and $4$ .

$\sqrt{7 d + 1} = 15$

Step 2

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

${\sqrt{7 d + 1}}^{2} = 15^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 d + 1}$ as ${(7 d + 1)}^{\frac{1}{2}}$ .

${({(7 d + 1)}^{\frac{1}{2}})}^{2} = 15^{2}$

Simplify the left side.

Simplify ${({(7 d + 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(7 d + 1)}^{\frac{1}{2}})}^{2}$ .

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

${(7 d + 1)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(7 d + 1)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Rewrite the expression.

${(7 d + 1)}^{1} = 15^{2}$

Simplify.

$7 d + 1 = 15^{2}$

Simplify the right side.

Raise $15$ to the power of $2$ .

$7 d + 1 = 225$

Step 4

Solve for $d$ .

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

Subtract $1$ from both sides of the equation.

$7 d = 225 - 1$

Subtract $1$ from $225$ .

$7 d = 224$

Divide each term in $7 d = 224$ by $7$ and simplify.

Divide each term in $7 d = 224$ by $7$ .

$\frac{7 d}{7} = \frac{224}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 d}{7} = \frac{224}{7}$

Divide $d$ by $1$ .

$d = \frac{224}{7}$

Simplify the right side.

Divide $224$ by $7$ .

$d = 32$

Solve for d square root of 7d+1-4=11

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