Algebra Examples

$11 x^{2} = x^{2} + 8 x$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

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

$11 x^{2} - x^{2} = 8 x$

Step 1.2

Subtract $8 x$ from both sides of the equation.

$11 x^{2} - x^{2} - 8 x = 0$

Step 2

Subtract $x^{2}$ from $11 x^{2}$ .

$10 x^{2} - 8 x = 0$

Step 3

Factor $2 x$ out of $10 x^{2} - 8 x$ .

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Step 3.1

Factor $2 x$ out of $10 x^{2}$ .

$2 x (5 x) - 8 x = 0$

Step 3.2

Factor $2 x$ out of $- 8 x$ .

$2 x (5 x) + 2 x (- 4) = 0$

Step 3.3

Factor $2 x$ out of $2 x (5 x) + 2 x (- 4)$ .

$2 x (5 x - 4) = 0$

Step 4

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

$x = 0$

$5 x - 4 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $5 x - 4$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $5 x - 4$ equal to $0$ .

$5 x - 4 = 0$

Step 6.2

Solve $5 x - 4 = 0$ for $x$ .

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Step 6.2.1

Add $4$ to both sides of the equation.

$5 x = 4$

Step 6.2.2

Divide each term in $5 x = 4$ by $5$ and simplify.

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Step 6.2.2.1

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $5$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{5}$

Step 7

The final solution is all the values that make $2 x (5 x - 4) = 0$ true.

$x = 0, \frac{4}{5}$