Find the Roots (Zeros) 5+x^2=(x+1)(x+6)

$5 + x^{2} = (x + 1) (x + 6)$

Step 1

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

$(x + 1) (x + 6) = 5 + x^{2}$

Step 2

Simplify $(x + 1) (x + 6)$ .

Rewrite.

$0 + 0 + (x + 1) (x + 6) = 5 + x^{2}$

Simplify by adding zeros.

$(x + 1) (x + 6) = 5 + x^{2}$

Expand $(x + 1) (x + 6)$ using the FOIL Method.

Apply the distributive property.

$x (x + 6) + 1 (x + 6) = 5 + x^{2}$

Apply the distributive property.

$x \cdot x + x \cdot 6 + 1 (x + 6) = 5 + x^{2}$

Apply the distributive property.

$x \cdot x + x \cdot 6 + 1 x + 1 \cdot 6 = 5 + x^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 6 + 1 x + 1 \cdot 6 = 5 + x^{2}$

Move $6$ to the left of $x$ .

$x^{2} + 6 \cdot x + 1 x + 1 \cdot 6 = 5 + x^{2}$

Multiply $x$ by $1$ .

$x^{2} + 6 x + x + 1 \cdot 6 = 5 + x^{2}$

Multiply $6$ by $1$ .

$x^{2} + 6 x + x + 6 = 5 + x^{2}$

Add $6 x$ and $x$ .

$x^{2} + 7 x + 6 = 5 + x^{2}$

Step 3

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

Subtract $x^{2}$ from both sides of the equation.

$x^{2} + 7 x + 6 - x^{2} = 5$

Combine the opposite terms in $x^{2} + 7 x + 6 - x^{2}$ .

Subtract $x^{2}$ from $x^{2}$ .

$7 x + 6 + 0 = 5$

Add $7 x + 6$ and $0$ .

$7 x + 6 = 5$

Step 4

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

Subtract $6$ from both sides of the equation.

$7 x = 5 - 6$

Subtract $6$ from $5$ .

$7 x = - 1$

Step 5

Divide each term in $7 x = - 1$ by $7$ and simplify.

Divide each term in $7 x = - 1$ by $7$ .

$\frac{7 x}{7} = \frac{- 1}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 1}{7}$

Divide $x$ by $1$ .

$x = \frac{- 1}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{7}$

Step 6

Find the Roots (Zeros) 5+x^2=(x+1)(x+6)

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