Solve Using the Quadratic Formula x-10 square root of x+9=0

$x - 10 \sqrt{x} + 9 = 0$

Step 1

Move all terms not containing $- 10 \sqrt{x}$ to the right side of the equation.

Subtract $x$ from both sides of the equation.

$- 10 \sqrt{x} + 9 = - x$

Subtract $9$ from both sides of the equation.

$- 10 \sqrt{x} = - x - 9$

Step 2

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

${(- 10 \sqrt{x})}^{2} = {(- x - 9)}^{2}$

Step 3

Simplify each side of the equation.

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

${(- 10 x^{\frac{1}{2}})}^{2} = {(- x - 9)}^{2}$

Simplify the left side.

Simplify ${(- 10 x^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 10 x^{\frac{1}{2}}$ .

${(- 10)}^{2} {(x^{\frac{1}{2}})}^{2} = {(- x - 9)}^{2}$

Raise $- 10$ to the power of $2$ .

$100 {(x^{\frac{1}{2}})}^{2} = {(- x - 9)}^{2}$

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

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

$100 x^{\frac{1}{2} \cdot 2} = {(- x - 9)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$100 x^{\frac{1}{2} \cdot 2} = {(- x - 9)}^{2}$

Rewrite the expression.

$100 x^{1} = {(- x - 9)}^{2}$

Simplify.

$100 x = {(- x - 9)}^{2}$

Simplify the right side.

Simplify ${(- x - 9)}^{2}$ .

Rewrite ${(- x - 9)}^{2}$ as $(- x - 9) (- x - 9)$ .

$100 x = (- x - 9) (- x - 9)$

Expand $(- x - 9) (- x - 9)$ using the FOIL Method.

Apply the distributive property.

$100 x = - x (- x - 9) - 9 (- x - 9)$

Apply the distributive property.

$100 x = - x (- x) - x \cdot - 9 - 9 (- x - 9)$

Apply the distributive property.

$100 x = - x (- x) - x \cdot - 9 - 9 (- x) - 9 \cdot - 9$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$100 x = - 1 \cdot - 1 x \cdot x - x \cdot - 9 - 9 (- x) - 9 \cdot - 9$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$100 x = - 1 \cdot - 1 (x \cdot x) - x \cdot - 9 - 9 (- x) - 9 \cdot - 9$

Multiply $x$ by $x$ .

$100 x = - 1 \cdot - 1 x^{2} - x \cdot - 9 - 9 (- x) - 9 \cdot - 9$

Multiply $- 1$ by $- 1$ .

$100 x = 1 x^{2} - x \cdot - 9 - 9 (- x) - 9 \cdot - 9$

Multiply $x^{2}$ by $1$ .

$100 x = x^{2} - x \cdot - 9 - 9 (- x) - 9 \cdot - 9$

Multiply $- 9$ by $- 1$ .

$100 x = x^{2} + 9 x - 9 (- x) - 9 \cdot - 9$

Multiply $- 1$ by $- 9$ .

$100 x = x^{2} + 9 x + 9 x - 9 \cdot - 9$

Multiply $- 9$ by $- 9$ .

$100 x = x^{2} + 9 x + 9 x + 81$

Add $9 x$ and $9 x$ .

$100 x = x^{2} + 18 x + 81$

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.

$x^{2} + 18 x + 81 = 100 x$

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

Subtract $100 x$ from both sides of the equation.

$x^{2} + 18 x + 81 - 100 x = 0$

Subtract $100 x$ from $18 x$ .

$x^{2} - 82 x + 81 = 0$

Factor $x^{2} - 82 x + 81$ 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 $81$ and whose sum is $- 82$ .

$- 81, - 1$

Write the factored form using these integers.

$(x - 81) (x - 1) = 0$

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

$x - 81 = 0$

$x - 1 = 0$

Set $x - 81$ equal to $0$ and solve for $x$ .

Set $x - 81$ equal to $0$ .

$x - 81 = 0$

Add $81$ to both sides of the equation.

$x = 81$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $(x - 81) (x - 1) = 0$ true.

$x = 81, 1$

Solve Using the Quadratic Formula x-10 square root of x+9=0

Related Questions

Support LCMGCF.com by disabling your adblocker.