Solve for x x+15=8 square root of x

$x + 15 = 8 \sqrt{x}$

Step 1

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

$8 \sqrt{x} = x + 15$

Step 2

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

${(8 \sqrt{x})}^{2} = {(x + 15)}^{2}$

Step 3

Simplify each side of the equation.

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

${(8 x^{\frac{1}{2}})}^{2} = {(x + 15)}^{2}$

Simplify the left side.

Simplify ${(8 x^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $8 x^{\frac{1}{2}}$ .

$8^{2} {(x^{\frac{1}{2}})}^{2} = {(x + 15)}^{2}$

Raise $8$ to the power of $2$ .

$64 {(x^{\frac{1}{2}})}^{2} = {(x + 15)}^{2}$

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

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

$64 x^{\frac{1}{2} \cdot 2} = {(x + 15)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$64 x^{\frac{1}{2} \cdot 2} = {(x + 15)}^{2}$

Rewrite the expression.

$64 x^{1} = {(x + 15)}^{2}$

Simplify.

$64 x = {(x + 15)}^{2}$

Simplify the right side.

Simplify ${(x + 15)}^{2}$ .

Rewrite ${(x + 15)}^{2}$ as $(x + 15) (x + 15)$ .

$64 x = (x + 15) (x + 15)$

Expand $(x + 15) (x + 15)$ using the FOIL Method.

Apply the distributive property.

$64 x = x (x + 15) + 15 (x + 15)$

Apply the distributive property.

$64 x = x \cdot x + x \cdot 15 + 15 (x + 15)$

Apply the distributive property.

$64 x = x \cdot x + x \cdot 15 + 15 x + 15 \cdot 15$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$64 x = x^{2} + x \cdot 15 + 15 x + 15 \cdot 15$

Move $15$ to the left of $x$ .

$64 x = x^{2} + 15 \cdot x + 15 x + 15 \cdot 15$

Multiply $15$ by $15$ .

$64 x = x^{2} + 15 x + 15 x + 225$

Add $15 x$ and $15 x$ .

$64 x = x^{2} + 30 x + 225$

Step 4

Solve for $x$ .

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} + 30 x + 225 = 64 x$

Move all terms containing $x$ to the left side of the equation.

Subtract $64 x$ from both sides of the equation.

$x^{2} + 30 x + 225 - 64 x = 0$

Subtract $64 x$ from $30 x$ .

$x^{2} - 34 x + 225 = 0$

Factor $x^{2} - 34 x + 225$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $225$ and whose sum is $- 34$ .

$- 25, - 9$

Write the factored form using these integers.

$(x - 25) (x - 9) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 25 = 0$

$x - 9 = 0$

Set $x - 25$ equal to $0$ and solve for $x$ .

Set $x - 25$ equal to $0$ .

$x - 25 = 0$

Add $25$ to both sides of the equation.

$x = 25$

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

The final solution is all the values that make $(x - 25) (x - 9) = 0$ true.

$x = 25, 9$

Solve for x x+15=8 square root of x

Related Questions

Support LCMGCF.com by disabling your adblocker.